Mobile vehicle

ABSTRACT

In a mobile vehicle  1  having a vehicle body  2 , a front wheel  3   f , and a rear wheel  3   r , the steering control wheel  3   f  can be steered by a steering actuator  8  about a steering axis Csf which is tilted backward. The steering actuator  8  is controlled by a control device  15 . The height a, from a ground surface  110 , of the intersection point Ef of the steering axis Csf of the steering control wheel  3   f  and a virtual straight line connecting the ground contact point of the steering control wheel  3   f  and the center of axle of the steering control wheel  3   f  in a basic posture state of the mobile vehicle  1  is set to satisfy a prescribed condition.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a mobile vehicle (mobile object) suchas a two-wheeled vehicle having a front wheel and a rear wheel.

2. Description of the Related Art

In a mobile vehicle, for example a motorcycle, having a front wheel anda rear wheel arranged spaced apart from each other in the longitudinaldirection of the vehicle body, the front wheel usually serves as asteering control wheel. In order to enhance the straight travelingproperty of the motorcycle, the steering axis of the front wheel(rotational axis of steering of the front wheel) is tilted backward(with a positive caster angle). Further, the axle of the front wheel isarranged on, or slightly behind, the steering axis.

As a result, a motorcycle of this type usually has a large positivetrail. It should be noted that having a positive trail means that thepoint of intersection of the steering axis and the ground surface withwhich the wheels come into contact lies in front of the ground contactpoint of the steering control wheel.

Further, as a motorcycle of this type, a motorcycle which is configuredsuch that the rear wheel is passively steered by a reaction force thatthe rear wheel receives from the road surface when the motorcycle makesa turn is also known, as seen, for example, in Japanese PatentApplication Laid-Open No. 04-224488.

SUMMARY OF THE INVENTION

For two-wheeled vehicles such as motorcycles, it is desired to enhancethe stability of the posture of the vehicle body particularly when thevehicle is stopped or traveling at a low speed.

In view of the foregoing, it is an object of the present invention toprovide a mobile vehicle which is capable of enhancing the stability ofthe posture of the vehicle body by steering of a front wheel or a rearwheel.

First of all, the fundamental technical matters related to the presentinvention will be described with reference to FIGS. 1 to 10.

FIG. 1 is a schematic side view of a two-wheeled vehicle 1(specifically, the two-wheeled vehicle 1 in the basic posture state aswill be described later) which is a mobile vehicle having a vehicle body2 and a front wheel 3 f and a rear wheel 3 r arranged spaced apart fromeach other in the longitudinal direction of the vehicle body 2. In FIG.1, besides the side view of the two-wheeled vehicle 1, the rear wheel 3r as seen from the back of the two-wheeled vehicle 1 is illustrated onthe left side of the two-wheeled vehicle 1, and the front wheel 3 f asseen from the front of the two-wheeled vehicle 1 is illustrated on theright side of the two-wheeled vehicle 1.

The front wheel 3 f is axially supported in a rotatable manner by afront-wheel support mechanism 4 provided at the front portion of thevehicle body 2. The front-wheel support mechanism 4 is made up, forexample, of a front fork. The front wheel 3 f is a steering controlwheel which can be steered (turned) about a steering axis Csf which istilted backward.

It should be noted that the steering axis Csf being tilted backwardmeans that the steering axis Csf extends obliquely with respect to thelongitudinal direction and up-and-down direction of the vehicle body 2such that the steering axis Csf has its upper portion located rearwardrelative to its lower portion in the front-rear (longitudinal) directionof the vehicle body 2.

The rear wheel 3 r is axially supported in a rotatable manner by arear-wheel support mechanism 5 provided at the rear portion of thevehicle body 2. The rear-wheel support mechanism 5 is made up, forexample, of a swing arm. This rear wheel 3 r is a non-steering controlwheel.

It is here assumed that a two-wheeled vehicle 1 which is in the state ofstanding still in the straight-ahead posture on a flat ground surface110, as shown in the figure, is regarded as one rigid body. It should benoted that the state in which the two-wheeled vehicle 1 is standingstill in the straight-ahead posture means the state in which the frontwheel 3 f and the rear wheel 3 r are both stationary in the uprightposture in contact with the ground surface 110 and in which the axlecenterlines (centers of rotational axes) Cf and Cr of the front wheel 3f and the rear wheel 3 r extend in parallel with each other in thedirection orthogonal to the longitudinal direction of the vehicle body2. Hereinafter, the state in which the two-wheeled vehicle 1 is standingstill in the straight-ahead posture as described above will be referredto as the “basic posture state” of the two-wheeled vehicle 1.

In the state where the two-wheeled vehicle 1 in the basic posture stateis regarded as one rigid body, the overall mass of the two-wheeledvehicle 1 (hereinafter, also simply referred to as “total mass”) isdenoted as m, the height of the overall center of gravity G of thetwo-wheeled vehicle 1 (hereinafter, also simply referred to as“center-of-gravity height”) is denoted as h, and the overall inertiamoment of the two-wheeled vehicle 1 (hereinafter, also simply referredto as “overall inertia”) about the longitudinal axis Crol (hereinafter,referred to as “central roll axis Crol”) which extends in thelongitudinal direction of the vehicle body 2 while passing through theoverall center of gravity G is denoted as I.

m: total massh: center-of-gravity heightI: overall inertia

Here, the length Lb defined by the following expression (1) will becalled “overall radius of inertia”. In the present specification, “*” isan arithmetic sign representing multiplication.

I=m*Lb*Lb  (1)

Lb: overall radius of inertia

With the overall radius of inertia Lb thus defined, a system having thetotal mass of m, overall inertia of I, and center-of-gravity height of h(the system obtained by regarding the two-wheeled vehicle 1 as one rigidbody; hereinafter, this system may also be referred to as “two-wheeledvehicle rigid body system”) is represented by a model (hereinafter,referred to as “first model”) shown in FIG. 2A.

The first model is a model which represents a two-wheeled vehicle rigidbody system as a system (mass point system) configured with two masspoints 121 and 122 each having an equal mass of m/2. In this firstmodel, the two mass points 121 and 122 are arranged such that a heightof their midpoint (height of the center of gravity of the mass points121 and 122) from the ground surface 110 coincides with thecenter-of-gravity height h of the overall center of gravity G and thatthe distance from each mass point 121, 122 to the midpoint matches theoverall radius of inertia Lb defined by the aforesaid expression (1).

The first model described above can be equivalently transformed to amodel (hereinafter, referred to as “second model”) shown in FIG. 2B.

The second model is a model which represents a two-wheeled vehicle rigidbody system as a system (mass point system) configured with two masspoints of a first mass point 123 and a second mass point 124. In thiscase, the second mass point 124 is located on the ground surface 110.That is, the height of the second mass point 124 from the ground surface110 is “0”.

In the second model, as shown below, the mass of the first mass point123 is represented as m1, the mass of the second mass point 124 as m2,the height of the first mass point 123 from the ground surface 110 ash′, and the difference c (=h′−h) between the height h′ and thecenter-of-gravity height h of the overall center of gravity G as c(where c>0). In other words, the height h′ of the first mass point 123from the ground surface 110 is represented as (h+c).

m1: mass of the first mass point 123m2: mass of the second mass point 124h′: height of the first mass point 123c: difference between the height h′ of the first mass point 123 and thecenter-of-gravity height h (where c>0)

The condition that the overall mass in the second model agrees with theoverall mass (=total mass m) in the first model is expressed by thefollowing expression (2).

m1+m2=m  (2)

The condition that the height of the center of gravity of the masspoints 123 and 124 in the second model agrees with the height of thecenter of gravity (=center-of-gravity height h) of the mass points 121and 122 in the first model is expressed by the following expression (3).

m1*c=m2*h  (3)

The condition that the inertia moment about the overall center ofgravity (specifically, the inertia moment about the aforesaid centralroll axis Crol) in the second model agrees with the inertia moment aboutthe center of gravity of the mass points 121 and 122 (=overall inertiaI) in the first model is expressed by the following expression (4).

m1*c*c+m2*h*h=I  (4)

From the above expressions (1) to (4), the following expressions (5a),(6a), and (7a) are obtained.

c=Lb*Lb/h  (5a)

m1=(h/(h+Lb*Lb/h))*m  (6a)

m2=((Lb*Lb/h)/(h+Lb*Lb/h))*m  (7a)

When the values of c, m1, and m2 are set as above, the second modelbecomes a model which has been equivalently transformed from the firstmodel. Accordingly, the two-wheeled vehicle rigid body system can alsobe expressed by the second model, instead of the first model.

According to the above expression (1), Lb*Lb=I/m. Therefore, theexpressions (5a), (6a), and (7a) can be rewritten to the followingexpressions (5b), (6b), and (7b), respectively. Therefore, the secondmodel is, in other words, a model of a two-wheeled vehicle rigid bodysystem which has a first mass point 123 whose height h′ from the groundsurface 110 is higher than the center-of-gravity height h of thetwo-wheeled vehicle 1 in the basic posture state, and a second masspoint 124 on the ground surface 110 (mass point 124 whose height fromthe ground surface 110 is “0”), and in which the difference c (=h′−h)between the height h′ of the first mass point 123 and thecenter-of-gravity height h and the masses m1 and m2 are set by thefollowing expressions (5b), (6b), and (7b) in accordance with the totalmass m, overall inertia I, and center-of-gravity height h of thetwo-wheeled vehicle 1.

c=I/(m*h)  (5b)

m1=(h/(h+I/(m*h)))*m  (6b)

m2=((I/(m*h))/(h+I/(m*h)))*m  (7b)

FIG. 3 shows an approximate dynamics model which approximately expressesthe dynamics of the two-wheeled vehicle 1 in the aforesaid basic posturestate and similar posture states (close to the basic posture state).This approximate dynamics model has been established by regarding thetwo-wheeled vehicle 1 as a two-wheeled vehicle rigid body system havingthe mass points 123 and 124 in the aforesaid second model.

It is here assumed a three-axis orthogonal coordinate system (XYZcoordinate system) in which a projected point obtained by projecting theoverall center of gravity G of the two-wheeled vehicle 1 in the basicposture state onto the ground surface 110 in the perpendicular direction(up-and-down direction) is defined as the origin, the longitudinaldirection of the vehicle body 2 of the two-wheeled vehicle 1 as theX-axis direction, the lateral direction (vehicle width direction) as theY-axis direction, and the vertical direction as the Z-axis direction. Inthis case, the positive directions of the X, Y, and Z axes correspond tothe forward, leftward, and upward directions, respectively.

Further, in terms of rotation or angle, the direction about the X axisis called the roll direction, the direction about the Y axis is calledthe pitch direction, and the direction about the Z axis is called theyaw direction. The positive directions of the roll, pitch, and yawdirections are each determined as the direction of rotation of aright-hand screw when the screw is turned so as to move in the positivedirection of the corresponding one of the X, Y, and Z axes.

In the case where the two-wheeled vehicle 1 makes a small motion fromthe basic posture state, the rotation of each of the front wheel 3 f andthe rear wheel 3 r about the corresponding axle centerline Cf, Cr issmall. Therefore, in the following consideration, the gyroscopic effectby the rotations (small rotations) of the front wheel 3 f and the rearwheel 3 r about their axle centerlines Cf and Cr are considered to beignorable.

Further, the caster angle of the front wheel 3 f (the inclination angle(with respect to the up-and-down direction) of the steering axis Csf ofthe front wheel 3 f in the basic posture state) is denoted as θcf. Inthis case, the caster angle θcf in the case where the steering axis Csfof the front wheel 3 f is tilted backward as shown in FIG. 1 is definedto be positive.

Supplementally, in an actual two-wheeled vehicle 1, the center ofgravity of the front wheel 3 f is generally eccentric from the steeringaxis Csf and, therefore, the steering (turning about the steering axisCsf) of the front wheel 3 f causes translational force (inertial force)in the Y-axis direction to be generated at the center of gravity of thefront wheel 3 f.

The magnitude of this translational force is obtained as a product ofthe amount of eccentricity of the center of gravity of the front wheel 3f from the steering axis Csf, the mass of the front wheel 3 f, and thesteering angular acceleration (rotational angular acceleration about thesteering axis Csf). However, it is considered that the effect of thistranslational force is ignorable, because the mass of the front wheel 3f is sufficiently small compared to the total mass m.

Further, due to the fact that the caster angle θcf is not “0”, when thefront wheel 3 f is steered about the steering axis Csf, a rotationalmotion component in the roll direction of the front wheel 3 f isgenerated. This results in generation of an inertial force moment(specifically, moment in the direction about the X axis due to theinertial force) of the front wheel 3 f.

The magnitude of this inertial force moment is obtained as a product ofthe inertia moment (inertia) of the front wheel 3 f about an axis whichpasses through the center of gravity of the front wheel 3 f and extendsin parallel with the X axis, the sine value sin(θcf) of the caster angleθcf, and the steering angular acceleration of the front wheel 3 f.However, the inertia moment of the front wheel 3 f is sufficiently smallcompared to the overall inertia I. Therefore, it is considered that theeffect of this inertial force moment is also ignorable.

It is now assumed that, in the basic posture state of the two-wheeledvehicle 1, the steering angle of the front wheel 3 f (hereinafter, alsosimply referred to as “front-wheel steering angle”) is changedinstantaneously from “0” to of (≠0). It is defined that the front-wheelsteering angle is “0” in the basic posture state (non-steered state ofthe front wheel 3 f). It is also defined that the positive rotationaldirection of the front-wheel steering angle (rotational angle) about thesteering axis Csf corresponds to the direction of rotation that makesthe front end of the front wheel 3 f turn left with respect to thevehicle body 2 (so that the two-wheeled vehicle 1 turns to the left whentraveling forward).

As shown in FIG. 4, the inclination angle in the roll direction(hereinafter, also referred to as “roll angle”) of the vehicle body 2immediately after the instantaneous change of the front-wheel steeringangle from “0” to δf (≠0) is denoted as φb, and the movement amount inthe Y-axis direction of the second mass point 124 is denoted as q.

According to the dynamic relationship, the moment generated about the Xaxis by the resultant force of a reaction force that the two-wheeledvehicle 1 receives from the ground surface 110 and an inertial forceresulting from the motions of the mass points 123 and 124 is “0”.

Here, the reaction force that the two-wheeled vehicle 1 receives fromthe ground surface 110 is composed of a reaction force in the verticaldirection (vertical load) and a friction force in the horizontaldirection. The friction force, however, does not generate a moment inthe roll direction about the origin.

Further, when the front-wheel steering angle is changed, the groundcontact point (point of application of the reaction force in thevertical direction) moves by a finite distance. Immediately after theinstantaneous change of the front-wheel steering angle, however, thelapse time is infinitesimal. Therefore, a value obtained by timeintegration of the moment in the roll direction generated by thereaction force in the vertical direction is infinitesimal. That is,immediately after the instantaneous change of the front-wheel steeringangle, the total angular momentum (in the roll direction) about theorigin due to the motions of the mass points 123 and 124 isinfinitesimal.

Incidentally, the height of the second mass point 124 is “0”, and themotion of the second mass point 124 is limited to the transversedirection. Therefore, the angular momentum about the origin due to themotion of the second mass point 124 is “0”.

On the basis of the above, the angular momentum about the origin due tothe motion of the first mass point 123 becomes infinitesimal. That is,the first mass point 123 is instantaneously held still. As a result, therotation in the roll direction (change in roll angle) of the vehiclebody 2 is performed about the mass point 123. In other words, it can beconsidered that the position of the first mass point 123 is fixed at theinstant when the steering angle of the front wheel 3 f is changed fromthe basic posture state.

In this case, the movement amount q in the Y-axis direction(hereinafter, simply referred to as “lateral movement amount q”) of thesecond mass point 124 is expressed by the following expression (8).

q=(c+h)*φb  (8)

In the expression (8), it is considered that the magnitude of φb issufficiently small and that the following holds: sin(φb)≈φb.

The roll angle of the front wheel 3 f is denoted as φf, and the rollangle of the rear wheel 3 r is denoted as φr.

Since the caster angle θcf is not “0”, the steering of the front wheel 3f causes a rotational motion component in the roll direction to begenerated on the front wheel 3 f.

Therefore, the roll angle φf of the front wheel 3 f is obtainedapproximately by the following expression (9). In the expression (9),the magnitude of δf is considered to be sufficiently small.

φf=−sin(θcf)*δf+φb  (9)

Further, the roll angle φr of the rear wheel 3 r is obtained by thefollowing expression (10).

φr=φb  (10)

Further, as shown in FIG. 1, a distance in the longitudinal direction(in the X-axis direction) between the overall center of gravity G of thetwo-wheeled vehicle 1 and the ground contact point of the front wheel 3f in the basic posture state is denoted as Lf, and a distance in thelongitudinal direction (in the X-axis direction) between the overallcenter of gravity G of the two-wheeled vehicle 1 and the ground contactpoint of the rear wheel 3 r in the basic posture state is denoted as Lr.That is, Lf represents the longitudinal distance between the center ofthe axle of the front wheel 3 f and the overall center of gravity G ofthe two-wheeled vehicle 1 in the basic posture state, and Lr representsthe longitudinal distance between the center of the axle of the rearwheel 3 r and the overall center of gravity G of the two-wheeled vehicle1 in the basic posture state.

Further, in the basic posture state, the point of intersection of thesteering axis Csf and a straight line connecting the center of the axleand the ground contact point of the front wheel 3 f is denoted as Ef,and the height of the intersection point Ef (height from the groundsurface 110) is denoted as a.

It should be noted that the height a of the intersection point Efindicates the position in the Z-axis direction (Z coordinate) of theintersection point Ef. When the intersection point Ef lies above theground surface 110, a>0; when the intersection point Ef lies below theground surface 110, a<0. Furthermore, in the case where the caster angleθcf is positive, the height a being positive means a positive trail (tshown in FIG. 1); whereas the height a being negative means a negativetrail t.

Further, as shown in FIG. 1, on a straight line connecting the center ofthe axle of the rear wheel 3 r and its ground contact point in the basicposture state, a point whose height from the ground surface 110coincides with the aforesaid height a is denoted as Er. The points Efand Er are fixed to the vehicle body 2. The line segment connectingthese points Ef and Er intersects the line segment connecting the masspoints 123 and 124 (i.e. the line segment which is orthogonal to the Xaxis and which passes through the overall center of gravity G). Thispoint of intersection is denoted as E, as shown in FIG. 1.

The movement amount in the Y-axis direction (lateral movement amount) ofthe point Ef at the time when the front wheel 3 f is instantaneouslysteered from the basic posture state is denoted as ef, and the movementamount in the Y-axis direction (lateral movement amount) of the point Erat that time is denoted as er. These ef and er are expressed by thefollowing expressions (11) and (12), respectively.

ef=−a*φf  (11)

er=−a*φr  (12)

In the expressions (11) and (12), it is considered that the magnitudesof φf and are sufficiently small and that the following hold:sin(φf)≈φf, sin(φr)≈φr.

The movement amount in the Y-axis direction (lateral movement amount) ofthe point E is denoted as e. As the point E is an internally dividingpoint between the points Ef and Er, the lateral movement amount e of thepoint E is expressed by the following expression (13).

e=(Lr/(Lf+Lr))*ef+(Lf/(Lf+Lr))*er  (13)

On the other hand, as shown in FIG. 4, the inclination of the linesegment connecting the point E and the second mass point 124 is equal tothe roll angle φb of the vehicle body 2. The height of the point E is a.Therefore, the following expression (14) holds. In the expression (14),it is considered that the magnitude of φb is sufficiently small and thatthe following holds: sin(φb)≈φb.

q=e+a*φb  (14)

From the above expressions (9) to (14), the following expression (15) isobtained.

q=Lr/(Lf+Lr)*a*sin(θcf)*δf  (15)

From the expressions (5a), (8), and (15), the following expression (16)is obtained.

φb=a*(Lr/((Lf+Lr)/(h+Lb*Lb/h)))*sin(θcf)*δf  (16)

As shown in FIG. 1 or 3, the radius of curvature of the transversecross-sectional shape of the front wheel 3 f at the position of theground contact point of the front wheel 3 f in the basic posture stateis denoted as Rf. Similarly, the radius of curvature of the transversecross-sectional shape of the rear wheel 3 r at the position of theground contact point of the rear wheel 3 r in the basic posture state isdenoted as Rr.

It should be noted that the above-described transverse cross-sectionalshape of the front wheel 3 f means the shape of the ground contact partas seen in a transverse cross section including the axle centerline Cfand the ground contact point of the front wheel 3 f (this corresponds tothe transverse cross-sectional shape of the ground contact part of thetire of the front wheel 30. The radius of curvature at the point ofcontact with the ground surface 110 in this transverse cross-sectionalshape is the above-described Rf. The same applies to the rear wheel 3 r.

The point of application, on the ground surface 110, of the resultantforce of the reaction force in the vertical direction which acts on thefront wheel 3 f from the ground surface 110 and the reaction force inthe vertical direction which acts on the rear wheel 3 r from the groundsurface 110, i.e. the center of contact pressure, is denoted as COP, andthe movement amount in the Y-axis direction (lateral movement amount) ofthe COP is denoted as p.

As shown in FIG. 5, the movement amount in the Y-axis direction of theground contact point of the front wheel 3 f is (−Rf*φf), and themovement amount in the Y-axis direction of the ground contact point ofthe rear wheel 3 r is (−Rr*φr). The example shown in FIG. 5 is the casewhere φr>0 and φf<0.

The COP is, as shown in FIG. 5, the point of intersection between the Yaxis and the line segment connecting the ground contact point of thefront wheel 3 f and the ground contact point of the rear wheel 3 r.Therefore, the lateral movement amount p of the COP is expressed by thefollowing expression (17).

p=−(Lr/(Lf+Lr))*Rf*φf−(Lf/(Lf+Lr))*Rr*φr  (17)

From the expressions (9), (10), and (17), the following expression (18)is obtained.

p=(Lr/(Lf+Lr))*Rf*sin(θcf)*δf−((Lf/(Lf+Lr))*Rr+(Lr/(Lf+Lr))*Rf)*φb  (18)

Supplementally, it can be interpreted that the part (Lr/(Lf+Lr))*Rf inthe first term on the right side of the expression (18) corresponds to avirtual tire radius (tire radius as seen on the plane orthogonal to theX axis) at the position immediately beneath the overall center ofgravity G corresponding to the roll angle resulting from the steering ofthe front wheel 3 f.

Further, it can be interpreted that the part((Lf/(Lf+Lr))*Rr+(Lr/(Lf+Lr))*Rf) in the second term on the right sideof the expression (18) corresponds to a virtual tire radius (tire radiusas seen on the plane orthogonal to the X axis) at the positionimmediately beneath the overall center of gravity G corresponding to theroll angle of the vehicle body 2.

Consideration will now be given to balancing in moment about the origin(of the XYZ coordinate system) immediately after the steering angle ofthe front wheel 3 f of the two-wheeled vehicle 1 in the basic posturestate is changed stepwise from “0” to δf (≠0) at a given initial timet0.

The dynamic behavior at this time can be expressed by a model shown inFIG. 6.

This model includes, as virtual components, a body link 132 which issupported on a dolly 131 movable in the Y axis direction, and a mobilesection 133 which is movably supported by the body link 132. The bodylink 132 and the mobile section 133 correspond to the vehicle body 2.

The Y axis is set above a floor 134 which supports the dolly 131. Thefloor 134 does not correspond to the actual ground surface 110 withwhich the two-wheeled vehicle 1 comes into contact. That is, the floor134 is simply a virtual plane that supports the dolly 131 to enable thedolly 131 to move in a horizontal direction. The actual ground surface110 exists at the level of the Y axis (the level where the Z coordinate(position coordinate in the Z-axis direction) becomes “0”).

In the model shown in FIG. 6, all the components are set to have theinertia moment of “0”. Of the components of this model, the componentsexcept the body link 132 and the mobile section 133 are set to have themass of “0”.

The body link 132 has a rail portion 132 a which extends in thetransverse direction and an erecting portion 132 b which extends upwardfrom the rail portion 132 a. The model has a first mass point 123 havinga mass m1 at the upper portion of the erecting portion 132 b. Before theinitial time t0, the Y coordinate of the position of the first masspoint 123 is “0”, and its Z coordinate is (h+c) (=h+Lb*Lb/h=h+I/(m*h)).

The body link 132 is connected via a link 136 to a member 135 which isfixedly secured to the floor 134. This constrains the movement in theY-axis direction of the body link 132; it cannot move in the Y-axisdirection. Before the initial time t0, the rail portion 132 a of thebody link 132 extends in the Y-axis direction.

The mobile section 133 is supported by the rail portion 132 a of thebody link 132 so as to be movable along the rail portion 132 a. Theposition in the Y-axis direction (Y coordinate) of this mobile section133 is controlled by an actuator 137 which is interposed between themobile section 133 and the erecting portion 132 b of the body link 132.

Further, the mobile section 133 has a second mass point 124 having amass m2. Before the initial time t0, the Z coordinate of the position ofthe mass point 124 is “0”.

The dolly 131 supporting the body link 132 is freely movable in ahorizontal direction on the floor 134. This dolly 131 has a wheel 131 aat its upper end, and is in contact (point contact) with the body link132 via the wheel 131 a, thereby supporting the body link 132 fromunderneath. The point of contact between the wheel 131 a of the dolly131 and the body link 132 corresponds to the aforesaid COP. With the COPas the fulcrum, the body link 132 can be inclined in the direction aboutthe X axis (roll direction).

The Z coordinate of the position of the COP is always “0”. Further, theY coordinate of the position of the COP is controlled by an actuator 138which is interposed between the lower portion of the rail portion 132 aof the body link 132 and the dolly 131. Supplementally, the inclinationin the direction about the X axis (roll direction) of the line segmentconnecting the first mass point 123 and the second mass point 124corresponds to the inclination in the direction about the X axis (rolldirection) of the vehicle body 2.

Before the initial time t0, the Y coordinate of the position of the COPand the Y coordinate of the position of the second mass point 124 areboth “0”.

It is here assumed that, with a stepwise change (from “0” to δf) of thefront-wheel steering angle at the initial time t0, the Y coordinate ofthe position of the COP has instantaneously become p by the actuator 138and the Y coordinate of the position of the second mass point 124 hasinstantaneously become q by the actuator 137.

Before the initial time t0, the Y coordinate of the position of thefirst mass point 123 is “0”. Further, instantaneously, the first masspoint 123 can be regarded as a fixed point, as stated above. Therefore,immediately after the initial time t0, the moment in the roll directionwhich is generated about the origin due to the gravitational forceacting on the first mass point 123 is “0”.

Further, the moment M2 (hereinafter, also referred to as “gravitationalmoment M2”) in the roll direction which is generated about the origindue to the gravitational force acting on the second mass point 124 isobtained by the following expression (19). It should be noted that grepresents the gravitational acceleration constant (>0). Further, thegravitational moment M2 corresponds to a second gravitational moment inthe present invention, as will be described later.

M2=−m2*g*q  (19)

Further, the moment Mp (hereinafter, also referred to as “road surfacereaction force moment Mp”) in the roll direction which is generatedabout the origin due to the road surface reaction force in the verticaldirection (vertical load) acting on the COP from the ground surface 110is obtained by the following expression (20).

Mp=m*g*p  (20)

According to the dynamic relationship, the sum of the above-describedmoments M2 and Mp coincides with the sign-reversed (or,opposite-polarity) total inertial force moment Ma in the roll directiongenerated about the origin due to the motions of the first mass point123 and the second mass point 124. That is, the following expression(21) holds.

Ma+M2+Mp=0  (21)

Consideration will now be given to the inertial force moment Ma.

The motions of the first mass point 123 and the second mass point 124are made up of the motion which is generated by the actuator 137 and themotion which is generated as the body link 132 inclines (rotates) in theroll direction about the COP.

The direction of the acceleration of the second mass point 124 generatedby the actuator 137 corresponds to the direction of the straight lineconnecting the second mass point 124 and the origin. Thus, the inertialforce moment in the roll direction generated about the origin due to themotion of the second mass point 124 by the actuator 137 is “0”.

Here, the rotational angular velocity of the body link 132 whichinclines in the roll direction about the COP is denoted as ω, and itsdifferential value (i.e. rotational angular acceleration) is denoted asωdot. The inertial force moment in the roll direction generated aboutthe origin due to the motions of the mass points 123 and 124 resultingfrom this rotational motion is obtained as a sum, multiplied by −1, ofthe square of the distance between the first mass point 123 and theorigin multiplied by the mass m1 and ωdot, and the square of thedistance between the second mass point 124 and the origin multiplied bythe mass m2 and ωdot.

The distance between the origin and the second mass point 124, however,is “0” before the initial time t0. Even after the initial time t0, it isconsidered that the distance between the origin and the second masspoint 124 (=absolute value of q) is sufficiently small compared to thedistance between the origin and the first mass point 123(=h+c=h+Lb*Lb/h). Further, the mass m2 is generally smaller than themass m1.

Therefore, the magnitude of the inertial force moment due to the motionof the second mass point 124 is sufficiently small compared to themagnitude of the inertial force moment due to the motion of the firstmass point 123, so that the inertial force moment due to the motion ofthe second mass point 124 can be ignored. Accordingly, Ma becomescomparable to the inertial force moment generated due to the motion ofthe first mass point 123 accompanying the inclination of the vehiclebody 2.

As a result, the total inertial force moment Ma in the roll directiongenerated about the origin is obtained by the following expression (22).

Ma=−m1*(h+Lb*Lb/h)*(h+Lb*Lb/h)*ωdot  (22)

From the expressions (21) and (22), the following expression (23) isobtained.

m1*(h+Lb*Lb/h)*(h+Lb*Lb/h)*ωdot=Mp+M2  (23)

The expression (23) can be interpreted that it expresses the behavior ofinclination of an inverted pendulum, having a mass m1 and a mass pointheight (h+Lb*Lb/h) and having the origin at the fulcrum, at the timewhen the moment (Mp+M2) is applied to the fulcrum of the invertedpendulum. Thus, hereinafter, the first mass point 123 may also bereferred to as “inverted pendulum mass point 123”.

Even if the body link 132 inclines in the roll direction about the COP,the position of the origin of the body link 132 hardly moves in thetransverse direction. Therefore, the inclination of the invertedpendulum mass point 123 coincides with the inclination in the rolldirection of the body link 132.

Further, the position of the fulcrum of the inverted pendulum mass point123 corresponds to the origin of the aforesaid three-axis orthogonalcoordinate system (the projected point obtained by projecting theoverall center of gravity G in the basic posture state of thetwo-wheeled vehicle 1 onto the ground surface 110 in the perpendiculardirection (up-and-down direction)).

Furthermore, since the first mass point (inverted pendulum mass point)123 and the second mass point 124 are on the plane of symmetry of thevehicle body 2 (plane of symmetry when the vehicle body 2 is consideredto be bilaterally symmetrical), the inclination in the roll direction ofthe line segment connecting the first mass point 123 and the second masspoint 124 corresponds to the inclination in the roll direction of thevehicle body 2 of the two-wheeled vehicle 1.

Further, as can be seen from the expression (15), the movement amount qin the Y-axis direction of the second mass point 124 is determineduniquely from the steering angle δf. It should be noted that in anactual two-wheeled vehicle such as the two-wheeled vehicle 1A in anembodiment which will be described later, the movement amount q isdetermined from the steering angle δf by a nonlinear function.

On the basis of the foregoing, stabilizing the motional state of theinverted pendulum mass point 123 while stabilizing the steering angle δfbecomes equivalent to stabilizing the inclination in the roll directionof the vehicle body 2 of the two-wheeled vehicle 1 while stabilizing thesteering angle δf.

It can be appreciated from the above expression (23) that the rotationalangular acceleration ωdot in the roll direction of the body link 132 (inother words, the rotational angular acceleration in the roll directionof the line segment connecting the origin and the inverted pendulum masspoint 123, or in yet other words, the rotational angular acceleration inthe roll direction of the inverted pendulum mass point 123 as seen fromthe origin) at the instant immediately after the initial time t0 isdetermined depending on: the aforesaid road surface reaction forcemoment Mp, which is generated about the origin due to the reaction forcein the vertical direction acting on the two-wheeled vehicle 1 from theground surface 110 via the COP, and the aforesaid gravitational momentM2, which is generated about the origin due to the gravitational forceacting on the second mass point 124.

Accordingly, it is possible to use (Mp+M2) as a manipulation moment forcontrolling the motional state of the inverted pendulum mass point 123.Consequently, it is possible to use (Mp+M2) as a manipulation moment forcontrolling the posture (inclination angle in the roll direction) of thevehicle body 2 of the two-wheeled vehicle 1 to a desired or requiredposture. Therefore, hereinafter, (Mp+M2) is denoted as Msum, as in thefollowing expression (24), and is called the “posture controllingmanipulation moment”.

Msum=Mp+M2  (24)

This posture controlling manipulation moment Msum is expressed by thefollowing expression (25) from the aforesaid expressions (1), (7), (15),(16), (18), (19), (20), and (24).

Msum=−(((Rg+I/(m*h))/(h+(I/(m*h)))*a−Rf)*(Lr/(Lf+Lr))*m*g*sin(θcf)*δf  (25)

where Rg=(Lr/(Lf+Lr))*Rf+(Lf/(Lf+Lr))*Rr  (25a)

As can be seen from the aforesaid expression (18), Rg corresponds to theratio of the amount of change in lateral movement amount p of the COP tothe amount of change in roll angle of the vehicle body 2 (i.e.sensitivity of the change in lateral movement amount p of the COP to asmall change in roll angle) in the case where the roll angle of thevehicle body 2 is changed by a small amount from the basic posturestate.

On the other hand, the gravitational moment M2 is expressed by thefollowing expression (26) from the aforesaid expressions (1), (7), (15),and (19).

M2=−((I/(m*h))/(h+I/(m*h)))*(Lr/(Lf+Lr))*a*m*g*sin(θcf)*δf  (26)

Further, the road surface reaction force moment Mp is expressed by thefollowing expression (27) from the aforesaid expressions (1), (16),(18), (20), and (25a).

Mp=−((Rg/(h+I/(m*h)))*a−Rf)*(Lr/(Lf+Lr))*m*g*sin(θcf)*δf  (27)

Here, a_sum, k_sum, a_p, k_p, and k_m are defined as follows.

a_sum=((h+I/(m*h))/(Rg+I/(m*h)))*Rf  (28)

k_sum=−((Rg+I/(m*h))/(h+I/(m*h)))*(Lr/(Lf+Lr))*m*g*sin(θcf)  (29)

k _(—) m=−((I/(m*h))/(h+I/(m*h)))*(Lr/(Lf+Lr))*m*g*sin(θcf)  (30)

a _(—) p=((h+I/(m*h))/Rg)*Rf  (31)

k _(—) p=−((Rg/(h+I/(m*h)))*(Lr/(Lf+Lr))*m*g*sin(θcf)  (32)

From the expressions (25), (28), and (29), the following expression (33)is obtained.

Msum=k_sum*(a−a_sum)*δf  (33)

Further, from the expressions (26) and (30), the following expression(34) is obtained.

M2=k _(—) m*a*δf  (34)

Further, from the expressions (27), (31), and (32), the followingexpression (35) is obtained.

Mp=k _(—) p*(a−a _(—) p)*δf  (35)

As can be seen from the expressions (33), (34), and (35), Msum, M2, andMp are proportional to the steering angle δf.

It should be noted that, from the expressions (28) and (31), thefollowing magnitude relationship holds between a_sum and a_p.

0<a_sum<a _(—) p  (36)

FIG. 7 is a graph showing the relationships between the height a andMsum/δf, M2/δf, and Mp/δf (indicated by the expressions (33), (34), and(35)).

Consideration will now be given to the relation between the settingvalue of the height a and the stability of the two-wheeled vehicle 1 ata standstill, with reference to FIG. 7.

First, the case is assumed where the height a coincides with a_sumdetermined by the expression (28) (the case where a=a_sum).

FIG. 8C illustrates the positional relationship between the second masspoint 124 and the COP in this case. In the illustrated example, it isassumed that δf>0. The same applies to FIGS. 8A, 8B, 8D, 9A, 9B, 9C, and9D, which will be explained later.

In the case where a=a_sum, the posture controlling manipulation momentMsum obtained by the aforesaid expression (33) is always “0”,irrespective of a change in front-wheel steering angle. Therefore, it isnot possible to control, using Msum, the motional state of the invertedpendulum mass point 123 (or the posture (inclination angle in the rolldirection) of the vehicle body 2 of the two-wheeled vehicle 1).

Next, the case is assumed where the height a is greater than a_sum andsmaller than a_p, as shown by the following expression (37).

a _(—) sum<a<a _(—) p  (37)

FIG. 8B illustrates the positional relationship between the second masspoint 124 and the COP in this case (δf>0 in the illustrated example). Inthis case, as shown in FIG. 7, Msum/δf takes a negative value.Therefore, when the steering angle δf is positive, Msum becomesnegative; when the steering angle δf is negative, Msum becomes positive.

Accordingly, it is theoretically possible to control the posture(inclination angle in the roll direction) of the vehicle body 2 of thetwo-wheeled vehicle 1 by manipulating the front-wheel steering angle.According to the experiments and studies conducted by the presentinventors, however, it has been found that the following disadvantagesarise in this case.

In the case where a_sum<a<a_p, as shown in FIG. 7, M2/δf and Mp/δfdiffer in polarity from each other, and the absolute value of M2/δf islarger than the absolute value of Mp/δf.

Therefore, the posture controlling manipulation moment Msum obtained bymanipulating the front-wheel steering angle depends primarily on M2.Further, Mp functions to disturb the control of the posture of thevehicle body 2 of the two-wheeled vehicle 1 by Msum generated in thesame direction as M2 (making the absolute value of Msum decreasedfurther than the absolute value of M2).

This means that, in order to generate the posture controllingmanipulation moment Msum of the magnitude sufficient for controlling theposture of the vehicle body 2 of the two-wheeled vehicle 1, thefront-wheel steering angle will have to be manipulated more largelycompared to the case where the assumption is made that Mp would notdisturb the control of the posture of the vehicle body 2 (i.e. the casewhere Mp=0, or Mp and M2 are in the same polarity).

That is, in the case where a_sum<a<a_p, when the posture (inclinationangle in the roll direction) of the vehicle body 2 of the two-wheeledvehicle 1 deviates from a desired or required posture, in order togenerate a restoring force for making the posture of the vehicle body 2restored to the required posture (that can stabilize the invertedpendulum mass point 123), it is necessary to considerably increase theabsolute value of the feedback gain for changing the front-wheelsteering angle in response to the change in inclination angle in theroll direction of the vehicle body 2 of the two-wheeled vehicle 1.

Incidentally, in the case where the front-wheel steering angle ischanged from the basic posture state of the two-wheeled vehicle 1 and,thus, the second mass point 124 is accelerated in the lateral directionof the two-wheeled vehicle 1, the inertial force generated by the secondmass point 124 by the acceleration is balanced with the friction forcewhich acts on the two-wheeled vehicle 1 from the ground surface 110.

The tires fitted to the front wheel 3 f and the rear wheel 3 r generallyundergo shear deformation in the transverse direction due to thefriction force received from the ground surface 110. This generallycauses a delay in response of the behavior of the second mass point 124to the change in front-wheel steering angle and, hence, a delay inresponse of the change of the gravitational moment M2 to the change infront-wheel steering angle.

Therefore, if the absolute value of the feedback gain for changing thefront-wheel steering angle in response to the change in inclinationangle of the vehicle body 2 of the two-wheeled vehicle 1 is set large,an oscillation phenomenon is likely to occur in the control system dueto the delay in response of the change of the gravitational moment M2and the delay in response of the inclination angle in the roll directionof the vehicle body 2 of the two-wheeled vehicle 1 to the change infront-wheel steering angle. This leads to degradation in robustness ofthe control of the posture of the vehicle body 2 by the manipulation ofthe front-wheel steering angle.

As such, when the posture controlling manipulation moment Msum becomeshighly dependent on M2, an oscillation phenomenon becomes more likely tooccur in the control system due to the effect of the delay in responseof the change of M2 attributable to the shear deformation of the tiresfitted to the front wheel 3 f and the rear wheel 3 r. That is, in thecase where a_sum<a<a_p, the oscillation phenomenon is likely to occur inthe control system due to the effect of the delay in response of thechange of M2 caused by the shear deformation of the tires.

Further, in the case where a_sum<a<a_p, at the time when the absolutevalue of the steering angle δf is large, it is difficult to stabilizethe control of the posture of the two-wheeled vehicle 1, for thefollowing reasons.

When the absolute value of the steering angle δf is large, the radius ofcurvature of the ground contact part of the steering control wheel(front wheel 3 f) as seen in a cross section including the groundcontact point of the steering control wheel (front wheel 3 f) and havinga normal corresponding to the X-axis direction (longitudinal directionof the vehicle body 2) becomes greater than the radius of curvature inthe case where the steering angle δf is “0”. Accordingly, thesubstantial Rf becomes larger as the absolute value of the steeringangle δf becomes larger. Further, Mp has dependency on Rf, as indicatedby the aforesaid expression (27).

FIG. 10 illustrates differences in graphs of Mp/δf due to thedifferences in magnitude of Rf. A straight line a 1 illustrates a graphof Mp/δf in the case where Rf takes a standard value (radius ofcurvature of the transverse cross-sectional shape of the front wheel 3 fat the position of the ground contact point of the front wheel 3 f inthe basic posture state), and a straight line α2 illustrates a graph ofMp/δf in the case where Rf is larger than the standard value. Further,a_p1 and a_p2 denote the values of a_p (values of a when Mp/δf is “0”)corresponding respectively to the straight lines α1 and α2.

As shown in FIG. 10, a_p2, i.e. the value of a_p when Rf is large, islarger than a_p1, i.e. the value of a_p when Rf is small. Further, theinclination of the straight line α2 when Rf is large is greater than theinclination of the straight line α1 when Rf is small.

Therefore, in the case where a takes a value satisfying a_sum<a<a_p,when Rf becomes larger, Mp/δf increases in the positive direction (thatis, it changes toward a direction of opposite polarity to that ofM2/δf). This causes Msum/δf to approach “0”, leading to degradation ofthe restoring force for making the posture of the vehicle body 2 of thetwo-wheeled vehicle 1 restored to a desired or required posture, or thepolarity of Msum/δf is reversed from negative to positive, making itdifficult to stabilize the control of the posture of the vehicle body 2.

As such, in the case where a_sum<a<a_p, when the absolute value of thesteering angle δf is large, it is difficult to stabilize the control ofthe motional state of the inverted pendulum mass point 123 (and, hence,the control of the posture of the vehicle body 2 of the two-wheeledvehicle 1) because the substantial Rf deviates from the Rf (standardvalue) in the basic posture state.

Next, the case is assumed where the height a is not smaller than a_p, asshown by the following expression (38).

a≧a _(—) p  (38)

FIG. 8A illustrates the positional relationship between the second masspoint 124 and the COP in this case (δf>0 in the illustrated example). Inthis case, as shown in FIG. 7, Msum/δf takes a negative value.Therefore, when the steering angle δf is positive, Msum becomesnegative; when the steering angle δf is negative, Msum becomes positive,as in the case where a_sum<a<a_p (in the case of FIG. 8B).

Accordingly, it is theoretically possible to control the motional stateof the inverted pendulum mass point 123 by manipulating the front-wheelsteering angle. Consequently, ft is possible to control the posture(inclination angle in the roll direction) of the vehicle body 2 of thetwo-wheeled vehicle 1 by the manipulation of the front-wheel steeringangle.

Further, in this case, M2/δf and Mp/δf will not become opposite inpolarity. That is, in the case where a=a_p, Mp/δf=0 and M2/δf<0. In thecase where a>a_p, M2/δf and Mp/δf are in the same polarity. Therefore,it is possible to generate the posture controlling manipulation momentMsum by M2 alone, or by cooperation of M2 and Mp.

This makes it possible to set the absolute value of the feedback gainfor the posture control of the vehicle body 2 to a value smaller than inthe case where a_sum<a<a_p (in the case of FIG. 8B).

However, since the absolute value of M2/δf is larger than the absolutevalue of Mp/δf, as shown in FIG. 7, Msum is highly dependent on M2.Further, since the height a is large, the lateral acceleration(acceleration in the Y-axis direction) of the second mass point 124tends to become large.

Therefore, the effect of the shear deformation of the tires fitted tothe front wheel 3 f and the rear wheel 3 r becomes large, as in the casewhere a_sum<a<a_p (in the case of FIG. 8B). The response of the changeof the gravitational moment M2 to the change of the front-wheel steeringangle is likely to delay, and accordingly, an oscillation phenomenon islikely to occur in the control system.

Next, the value of a which makes the following expression (39) hold isdenoted as a_s.

Msum=−M2  (39)

The state where the above expression (39) holds corresponds to the statewhere M2 functions to disturb the control of the posture of the vehiclebody 2 of the two-wheeled vehicle 1 by Msum (i.e. the direction of M2becomes opposite to the direction of Msum) and where the absolute valuesof M2 and Msum are equal to each other.

From the expressions (25) and (27), the above a_s is expressed by thefollowing expression (40).

a _(—) s=((h+I/(m*h))/(Rg+2*I/(m*h)))*Rf  (40)

From the fact that all the parameters on the right side of theexpression (40) are positive and from the aforesaid expressions (28) and(40), the relationship in the following expression (41) is obtained.

0<a _(—) s<a_sum  (41)

Next, the case is assumed where the height a is larger than a_s andsmaller than a_sum, as shown by the following expression (42).

a _(—) s<a<a_sum  (42)

FIG. 8D illustrates the positional relationship between the second masspoint 124 and the COP in this case (δf>0 in the illustrated example). Inthis case, Msum/δf (=Mp/δf+M2/δf) takes a positive value. In otherwords, Mp/δf>−M2/δf.

Therefore, when the steering angle of is positive, the posturecontrolling manipulation moment Msum becomes positive; when the steeringangle δf is negative, the posture controlling manipulation moment Msumbecomes negative. Accordingly, it is theoretically possible to controlthe motional state of the inverted pendulum mass point 123 bymanipulating the front-wheel steering angle. Consequently, it ispossible to control the posture (inclination angle in the directionabout the X axis) of the vehicle body 2 of the two-wheeled vehicle 1 bythe manipulation of the front-wheel steering angle.

In the case where a_s<a<a_sum, however, although the absolute value ofM2 becomes smaller than in the case where a>a_sum and the oscillation inthe control of the posture of the vehicle body 2 resulting from theshear deformation of the tires of the front wheel 3 f and the rear wheel3 r can be restricted, compared to the case where 0<a≦a_s which will bedescribed later, oscillation is still likely to occur in the control ofthe posture of the vehicle body 2 due to the shear deformation of thetires of the front wheel 3 f and the rear wheel 3 r, for the followingreasons.

In the case where a takes a value satisfying the expression (42),Msum/δf and M2/δf are opposite in polarity, as shown in FIG. 7. That is,M2 functions to disturb the control of the posture of the vehicle body 2by Msum. In addition, as explained above, M2 is accompanied by lateralacceleration due to the movement of the second mass point 124, causingshear deformation of the tires of the front wheel 3 f and the rear wheel3 r. Consequently, an oscillation phenomenon is likely to occur in thecontrol system because of the delay in response resulting from the sheardeformation.

Further, when a takes a value satisfying the expression (42), theabsolute value of Msum/δf is smaller than the absolute value of M2/δf.That is, the absolute value of the posture controlling manipulationmoment Msum becomes smaller than the absolute value of M2 which disturbsthe posture control of the vehicle body 2 and causes an oscillationphenomenon in the control system. Therefore, when the absolute value ofthe feedback gain is set to a relatively small value so as to avoid theoscillation phenomenon in the control system, the magnitude of theposture controlling manipulation moment Msum is likely to becomeinsufficient.

Next, the case is assumed where the height a is larger than “0” and notlarger than a_s, as shown by the following expression (43).

0<a≦a _(—) s  (43)

FIG. 9A illustrates the positional relationship between the second masspoint 124 and the COP in the case where a=a_s (δf>0 in the illustratedexample). FIG. 9B illustrates the positional relationship between thesecond mass point 124 and the COP in the case where 0<a<a_s (δf>0 in theillustrated example).

In the case where 0<a≦a_s, Msum/δf becomes positive, as shown in FIG. 7.Therefore, Msum becomes positive when the steering angle δf is positive,while Msum becomes negative when the steering angle δf is negative.

Further, in this case, Msum/δf and M2/δf are opposite in polarity, as inthe case where a_s<a<a_sum. That is, M2 functions to disturb the controlof the posture of the vehicle body 2 by Msum.

However, when a takes a value satisfying the expression (43), theabsolute value of Msum/δf becomes equal to or larger than the absolutevalue of M2/δf. In other words, Msum/δf>−M2/δf. That is, the absolutevalue of M2 which disturbs the posture control of the vehicle body 2 andcauses the oscillation phenomenon in the control system is kept at orbelow the absolute value of the posture controlling manipulation momentMsum.

Accordingly, even if the absolute value of the feedback gain is set to arelatively large value in order to cause a sufficiently large posturecontrolling manipulation moment Msum to be generated for making theposture (inclination angle in the roll direction) of the vehicle body 2restored to a required posture, oscillation is not likely to occur inthe control system. That is, it is possible to enhance the stability ofthe control of the motional state of the inverted pendulum mass point123 by the manipulation of the front-wheel steering angle (and, hence,the stability of the posture control of the vehicle body 2 of thetwo-wheeled vehicle 1).

Next, the case is assumed where the height a is “0” (in the case wherea=0).

FIG. 9C illustrates the positional relationship between the second masspoint 124 and the COP in this case (δf>0 in the illustrated example). Inthis case, as shown in FIG. 7, Msum/δf becomes positive. Thus, Msumbecomes positive when the steering angle δf is positive, while Msumbecomes negative when the steering angle δf is negative.

Further, in this case, M2 is always “0”. Therefore, the posturecontrolling manipulation moment Msum caused by the manipulation of thefront-wheel steering angle is generated by Mp alone. In this case, evenif the front-wheel steering angle is manipulated from the basic posturestate, the movement amount in the Y-axis direction of the second masspoint 124 is “0”, so that no friction force is generated to act on thetwo-wheeled vehicle 1 from the ground surface 110.

The tires of the front wheel 3 f and the rear wheel 3 r do not undergoshear deformation, and thus, an oscillation phenomenon in the controlsystem due to the shear deformation of the tires is unlikely to occur.Accordingly, it is possible to further increase the absolute value ofthe aforesaid feedback gain, than in the case where the value of asatisfies the aforesaid expression (43), to thereby increase therestoring force for making the motional state of the inverted pendulummass point 123 restored to the required state and also enhance thestability of the control of the motional state. Consequently, it ispossible to increase the restoring force for making the posture of thevehicle body 2 restored to the required posture and also enhance thestability of the control of the posture.

Further, since the magnitude of Msum which can be generated per unitchange amount of the front-wheel steering angle becomes larger than inthe case where the value of a satisfies the aforesaid expression (43),it is possible to decrease the change amount of the front-wheel steeringangle that is necessary for making the posture of the vehicle body 2restored to the required posture.

Next, the case is assumed where the height a is negative (in the casewhere a<0).

FIG. 9D illustrates the positional relationship between the second masspoint 124 and the COP in this case (δf>0 in the illustrated example). Inthis case, as shown in FIG. 7, Msum/δf becomes positive. Thus, theposture controlling manipulation moment Msum becomes positive when thesteering angle δf is positive, while the posture controllingmanipulation moment Msum becomes negative when the steering angle δf isnegative.

Further, in this case, M2/δf and Mp/δf are in the same polarity. Thisenables M2 and Mp to cooperate to generate the posture controllingmanipulation moment Msum. As a result, the magnitude of Msum that can begenerated per unit change amount of the front-wheel steering anglebecomes larger than in the case where a=0, and accordingly, it ispossible to still further decrease the magnitude of the change amount ofthe front-wheel steering angle necessary for making the posture of thevehicle body 2 restored to the required posture.

It can be said from the foregoing that, in the case of attempting tocontrol the posture (inclination angle in the roll direction) of thevehicle body 2 of the two-wheeled vehicle 1 to a required posture bysteering of the front wheel 3 f of the two-wheeled vehicle 1 (in thecase of attempting to control the motional state of the invertedpendulum mass point 123 in the dynamics model of the two-wheeled vehicle1), setting the arrangement position of the backwardly tilted steeringaxis Csf of the front wheel 3 f (steering control wheel) such that theheight a of the intersection point Ef of the steering axis Csf and thestraight line connecting the center of the axle of the front wheel 3 f(steering control wheel) and the ground contact point of the front wheel3 f becomes smaller than a_sum defined by the expression (28) is aprerequisite for stably controlling the motional state of the invertedpendulum mass point 123 (and, hence, the posture of the vehicle body 2).

In order to suppress the oscillation phenomenon in the control systemdue to the tire shear deformation, it is further preferable to set thearrangement position of the steering axis Csf such that the height abecomes not greater than a_s defined by the expression (40).

For still further decreasing the magnitude of the change amount of thefront-wheel steering angle necessary for making the posture of thevehicle body 2 restored to the required posture, it is furtherpreferable to set the arrangement position of the steering axis Csf suchthat the height a becomes “0” or takes a negative value.

The matters described above are related to the case of steering thefront wheel 3 f for controlling the posture of the vehicle body 2. Thesematters also apply to the case of steering a rear wheel for controllingthe posture (inclination angle in the roll direction) of a vehicle bodyin a two-wheeled vehicle (mobile vehicle) having a steerable rear wheel.

Hereinafter, a description will be made for a two-wheeled vehicle havinga steerable rear wheel. FIG. 11 schematically shows, as in FIG. 1, aside view of a two-wheeled vehicle 201 (in the basic posture state)which is a mobile vehicle having a vehicle body 202 and a front wheel203 f and a rear wheel 203 r arranged spaced apart from each other inthe longitudinal direction of the vehicle body 202, in which the rearwheel 203 r is steerable, a view of the rear wheel 203 r as seen fromthe back of the two-wheeled vehicle 201, and a view of the front wheel203 f as seen from the front of the two-wheeled vehicle 201.

It should be noted that the basic posture state of this two-wheeledvehicle 201 means a state similar to the basic posture state of thetwo-wheeled vehicle 1 in FIG. 1. That is, it means the state in whichthe front wheel 203 f and the rear wheel 203 r are both stationary inthe upright posture in contact with the ground surface 110 and in whichthe axle centerlines (centers of rotational axes) Cf and Cr of the frontwheel 203 f and the rear wheel 203 r extend in parallel with each otherin the direction orthogonal to the longitudinal direction of the vehiclebody 202 (the state in which the two-wheeled vehicle 201 is standingstill in the straight-ahead posture).

The rear wheel 203 r is axially supported in a rotatable manner by arear-wheel support mechanism 205 provided at the rear portion of thevehicle body 202. The rear-wheel support mechanism 205 is made up of amechanism, similar to the front fork or the like, which enables steeringof the rear wheel 203 r. This mechanism makes the rear wheel 203 r asteering control wheel which can be turned (steered) about a steeringaxis Csr.

The steering axis Csr for the rear wheel 203 r is tilted backward. Thatis, the steering axis Csr extends obliquely with respect to thelongitudinal direction and up-and-down direction of the vehicle body 202such that the steering axis Csr has its upper portion located rearwardrelative to its lower portion in the front-rear (longitudinal) directionof the vehicle body 202.

The front wheel 203 f is axially supported in a rotatable manner by afront-wheel support mechanism 204, made up of a front fork or the like,provided at the front portion of the vehicle body 202, as in thetwo-wheeled vehicle 1 shown in FIG. 1. The front wheel 203 f is asteering control wheel which can be turned (steered) about a steeringaxis Csf which is tilted backward.

In the two-wheeled vehicle 201 in FIG. 11 in which the rear wheel 203 ris steerable, the steering axis Csf of the front wheel 203 f does notnecessarily have to be tilted backward. Further, the front wheel 203 fdoes not necessarily have to be a steering control wheel.

In the two-wheeled vehicle 201 (hereinafter, also referred to as“rear-wheel steering two-wheeled vehicle 201”) having the steerable rearwheel 203 r as described above, as in the case of the two-wheeledvehicle 1 in FIG. 1 (hereinafter, also referred to as “front-wheelsteering two-wheeled vehicle 1”), the rear-wheel steering two-wheeledvehicle 201 in the basic posture state can be regarded as a rigid bodysystem (two-wheeled vehicle rigid body system) which is made up of twomass points of a first mass point 123 having a mass m1 and a second masspoint 124 having a mass m2, as shown in FIG. 12.

The masses m1 and m2 of the mass points 123 and 124, and a difference cbetween the height of the mass point 123 and the center-of-gravityheight h are defined by the aforesaid expressions (5a), (6a), and (7a),or by the expressions (5b), (6b), and (7b), as in the case of thefront-wheel steering two-wheeled vehicle 1 in FIG. 1.

It should be noted that the XYZ coordinate system in FIG. 12 is set in asimilar manner as in the case of the front-wheel steering two-wheeledvehicle 1.

Further, in this case, the dynamic behavior when, instead of steering ofthe front wheel 203 f, the steering angle (rotational angle about thesteering axis Csr) of the rear wheel 203 r is changed stepwise from “0”from the basic posture state of the rear-wheel steering two-wheeledvehicle 201 (i.e. the dynamic behavior related to the moment generatedabout the origin in the direction about the X axis (roll direction) ofthe XYZ coordinate system) is similar to that in the front-wheelsteering two-wheeled vehicle 1.

In more detail, the caster angle of the rear wheel 203 r (theinclination angle (with respect to the up-and-down direction) of thesteering axis Csr of the rear wheel 203 r in the basic posture state) isdenoted as θcr. In this case, the caster angle θcr in the case where thesteering axis Csr of the rear wheel 203 r is tilted backward as shown inFIG. 12 is defined to be positive.

Further, the value of the steering angle of the rear wheel 203 r(hereinafter, also simply referred to as “rear-wheel steering angle”)after a stepwise change is denoted as δr. In this case, it is definedthat the rear-wheel steering angle is “0” in the basic posture state(non-steered state of the rear wheel 203 r). It is also defined that thepositive rotational direction of the rear-wheel steering anglecorresponds to the direction of rotation that makes the front end of therear wheel 203 r turn left with respect to the vehicle body 202 (so thatthe two-wheeled vehicle 201 turns to the right when traveling forward).

Further, in the basic posture state of the rear-wheel steeringtwo-wheeled vehicle 201, as shown in FIG. 12, the height of anintersection point Er′ of the steering axis Csr and a straight lineconnecting the center of the axle of the rear wheel 203 r and its groundcontact point (height from the ground surface 110) is denoted as a′.

It should be noted that the height a′ of the intersection point Er′indicates the position in the Z-axis direction (Z coordinate). When theintersection point Er′ lies above the ground surface 110, a′>0; whereaswhen the intersection point Er′ lies below the ground surface 110, a′<0.Furthermore, in the case where the caster angle θcr of the rear wheel203 r is positive (i.e. when the steering axis Csr is tilted backward),the height a′ being positive means a positive trail (t′ shown in FIG.12); whereas the height a′ being negative means a negative trail t′.

Further, in FIGS. 11 and 12, Ef′ represents a point, on the straightline connecting the center of the axle of the front wheel 203 f and itsground contact point, at which the height from the ground surface 110agrees with the aforesaid height a′ in the basic posture state, and E′represents a point of intersection of the line segment connecting thepoints Ef′ and Er′ and the line segment connecting the mass points 123and 124 (supplementally, this line segment is orthogonal to the X axisand passes through the overall center of gravity G).

In the rear-wheel steering two-wheeled vehicle 201, when the parametersθcf, δf, and a in the above-described expressions related to thefront-wheel steering two-wheeled vehicle 1 are replaced with theabove-described θcr, δr, and a′, respectively, and when the suffixes rand f in Lf, Lr, Rf, Rr, φf, φr, ef, and er are replaced with eachother, then the expressions corresponding to the rear-wheel steeringtwo-wheeled vehicle 201 are obtained.

For example, the values for the rear-wheel steering two-wheeled vehicle201 corresponding to Msum, M2, Mp, a_sum, a_p, and a_s for thefront-wheel steering two-wheeled vehicle 1 are denoted as Msum′, M2′,Mp′, a_sum′, a_p′, and a_s′, respectively. At this time, for theaforesaid expressions (25), (26), (27), (28), (31), and (40) related toMsum, M2, Mp, a_sum, a_p, and a_s, the following expressions (25)′,(26)′, (27)′, (28)′, (31)′, and (40)′ related to Msum′, M2′, Mp′,a_sum′, a_p′, and a_s′ are obtained respectively.

Msum′=−(((Rg+I/(m*h))/(h+(I/(m*h)))*a′−Rr)*(Lf/(Lf+Lr))*m*g*sin(θcr)*δr  (25)′

where Rg=(Lr/(Lf+Lr))*Rf+(Lf/(Lf+Lr))*Rr  (25a)

M2′=−(I/(m*h))/(h+P(m*h)))*(Lf/(Lf+Lr))*a′*m*g*sin(θcr)*δr  (26)′

Mp′=−((Rg/(h+I/(m*h)))*a′−Rr)*(Lf/(Lf+Lr))*m*g*sin(θcr)*δr  (27)′

a_sum′=((h+I/(m*h))/(Rg+I/(m*h)))*Rr  (28)′

a _(—) p′=((h+I/(m*h))/Rg)*Rr  (31)′

a _(—) s′=((h+I/(m*h))/(Rg+2*I/(m*h)))*Rr  (40)′

It should be noted that m, I, h, Lf, Lr, Rf, Rr, and g in the aboveexpressions have the same meanings as in the case of the front-wheelsteering two-wheeled vehicle 1. Further, in the rear-wheel steeringtwo-wheeled vehicle 201, ef, er, and e expressed by the aforesaidexpressions (11), (12), and (13) indicate the movement amounts in theY-axis direction of the points Ef, Er′, and E′, respectively, shown inFIG. 11 or 12.

On the basis of the above, the behavior in the case of steering therear-wheel steering angle in the rear-wheel steering two-wheeled vehicle201 becomes similar to the behavior in the case of steering thefront-wheel steering angle in the front-wheel steering two-wheeledvehicle 1. Therefore, in the case of attempting to control the posture(inclination angle in the roll direction) of the vehicle body 202 of thetwo-wheeled vehicle 201 to a desired or required posture by steering ofthe rear wheel 203 r of the rear-wheel steering two-wheeled vehicle 201,the relationship between the stability of the control and the value ofa′ becomes similar to the relationship between the stability of thecontrol of the posture of the vehicle body 2 and the value of a in thefront-wheel steering two-wheeled vehicle 1.

Accordingly, it can be said that, in the case of attempting to controlthe posture (inclination angle in the roll direction) of the vehiclebody 202 of the rear-wheel steering two-wheeled vehicle 201 to arequired posture by steering of the rear wheel 203 r of the two-wheeledvehicle 201 (in the case of attempting to control the motional state ofthe inverted pendulum mass point 123 in the dynamics model of thetwo-wheeled vehicle 201), setting the arrangement position of thebackwardly tilted steering axis Csr of the rear wheel 203 r (steeringcontrol wheel) such that the height a′ of the intersection point Er′ ofthe steering axis Csr of the rear wheel 203 r (steering control wheel)and the straight line connecting the center of the axle of the rearwheel 203 r (steering control wheel) and the ground contact point of therear wheel 203 r becomes smaller than a_sum′ defined by the expression(28)′ is a prerequisite for stabilizing the motional state of theinverted pendulum mass point 123 (and, hence, stably controlling theposture of the vehicle body 202).

In order to suppress the oscillation phenomenon in the control systemdue to the tire shear deformation, it is further preferable to set thearrangement position of the steering axis Csr of the rear wheel 203 r(steering control wheel) such that the height a′ becomes not greaterthan a_s′ defined by the expression (40)′.

For still further decreasing the magnitude of the change amount of therear-wheel steering angle necessary for making the posture of thevehicle body 202 restored to the required posture, it is furtherpreferable to set the arrangement position of the steering axis Csr ofthe rear wheel 203 r (steering control wheel) such that the height a′becomes “0” or takes a negative value.

Supplementally, regarding the front-wheel steering two-wheeled vehicle1, Msum in the aforesaid expression (25), M2 in the expression (26), andMp in the expression (27) are each linear with respect to the steeringangle δf of the front wheel 3 f. Similarly, regarding the rear-wheelsteering two-wheeled vehicle 201, Msum′ in the aforesaid expression(25)′, M2′ in the expression (26)′, and Mp′ in the expression (27)′ areeach linear with respect to the steering angle δr of the rear wheel 203r.

Therefore, the posture controlling manipulation moment in the case ofcontrolling the posture of the vehicle body of the two-wheeled vehicleby steering both of the front and rear wheels is obtained as a sum ofMsum in the expression (25) and Msum′ in the expression (25)′.Similarly, the gravitational moment (moment in the roll directiongenerated about the origin due to the gravitational force) in the caseof steering both of the front and rear wheels is obtained as a sum of M2in the expression (26) and M2′ in the expression (26)′. Furthermore, theroad surface reaction force moment (moment in the roll directiongenerated about the origin due to the reaction force in the verticaldirection from the ground surface 110) in the case of steering both ofthe front and rear wheels is obtained as a sum of Mp in the expression(27) and Mp′ in the expression (27)′.

Incidentally, it can be considered in the front-wheel steeringtwo-wheeled vehicle 1 or the rear-wheel steering two-wheeled vehicle 201that it is practically impossible that the center-of-gravity height hbecomes equal to or lower than Rg defined by the aforesaid expression(25a).

Even assuming that the center-of-gravity height h is Rg or lower, inthis case, the two-wheeled vehicle 1 or 201 becomes dynamically stablein the basic posture state, without the need of posture control bysteering of the steering control wheel (front wheel 3 f or rear wheel203 r). Therefore, in discussing the stability of the posture control ofthe vehicle 2 or 202 by way of steering, it is only necessary toconsider the case where the value of the center-of-gravity height h isRg or larger.

In this case, for example regarding the front-wheel steering two-wheeledvehicle 1, the value of ((h+I/(m*h))/(Rg+I/(m*h))) becomes larger than1, so that the right side of the expression (28) becomes larger than Rf.That is, as long as h is larger than Rg, the value of a_sum determinedby the expression (28) becomes always larger than Rf with respect toarbitrary h, I, and m.

On the other hand, regarding the front-wheel steering two-wheeledvehicle 1, when the height a is smaller than a_sum, Mp/δf becomespositive, Mp/δf>(−M2/δf), and Msum/δf becomes positive, as explainedabove.

From the above, when a is set to Rf or lower, as long as h is largerthan Rg, Mp/δf becomes positive, Mp/δf>(−M2/δf), and Msum/δf becomespositive with respect to arbitrary h, I, and m.

That is, when a is set to Rf or lower, even in the case where the valuesof h, I, and m have not been calculated at the planning phase, or thevalues of h, I, and m have not been measured, or even in the case wherethe values of h, I, and m may vary because a given object may be mountedon or attached to the mobile vehicle, Mp/δf becomes always positive,Mp/δf becomes always greater than (−M2/δf), and Msum/δf becomes alwayspositive, as long as h is larger than Rg. Accordingly, it is possible tocause the posture controlling manipulation moment Msum for making theposture (inclination angle in the roll direction) of the vehicle body 2restored to a required posture to be generated in an appropriatedirection, independently of the values of h, I, and m.

It cannot be determined whether the posture controlling manipulationmoment Msum is sufficiently large, unless the values of h, I, and m areknown. However, even if the values of h, I, and m are unknown, onlychecking whether a is Rf or lower makes it possible to determine whetherthe posture controlling manipulation moment Msum for making the posturerestored to a required posture can be generated in an appropriatedirection. It is therefore possible to use the height a equal to orlower than Rf, as a design guideline for a two-wheeled vehicle 1.

The above-described matters also apply to the rear-wheel steeringtwo-wheeled vehicle 201. That is, when the height a′ is set to Rr orlower, as long as h is larger than Rg, the following always hold: Mp′/δris positive; Mp′/δr>(−M2′/δr); and Msum′/δr is positive. Accordingly, itis possible to cause the posture controlling manipulation moment Msum′for making the posture (inclination angle in the roll direction) of thevehicle body 202 restored to a required posture to be generated in anappropriate direction, independently of the values of h, I, and m.

In the above-described model for the front-wheel steering two-wheeledvehicle 1 shown in FIG. 1, the mass and the inertia moment (inertia)were concentrated on the vehicle body 2. In the model, the gravitationalforce which acts on a steering mobile section made up of the front wheel3 f and the front-wheel support mechanism 4, and the inertial force ofthe steering mobile section which is generated when the steering mobilesection makes a motion relative to the vehicle body 2 in accordance withthe steering of the front wheel 3 f were both ignored.

Similarly, in the model for the rear-wheel steering two-wheeled vehicle201 schematically shown in FIG. 11, the mass and the inertia moment(inertia) were concentrated on the vehicle body 202. In the model, thegravitational force which acts on a steering mobile section made up ofthe rear wheel 203 r and the rear-wheel support mechanism 205, and theinertial force of the steering mobile section which is generated whenthe steering mobile section makes a motion relative to the vehicle body202 in accordance with the steering of the rear wheel 203 r were bothignored.

For an ordinary two-wheeled vehicle, steering control of the steeringcontrol wheel (front wheel 3 f or rear wheel 203 r) based on the modelas described above ensures sufficient posture stabilizing control forthe vehicle body 2 or 202.

When accessory equipment such as audio equipment is attached to thefront-wheel support mechanism 4 (or rear-wheel support mechanism 205),however, the mass of the aforesaid steering mobile section may increase,the inertia moment of the steering mobile section about the steeringaxis Csf (or Csr) may increase, or the center of gravity of the steeringmobile section may greatly deviate from the steering axis Csf (or Csr).

In such a case, posture control with higher accuracy will be possiblewhen the two-wheeled vehicle is modeled by further taking into accountthe gravitational force which acts on the steering mobile section madeup of the front wheel 3 f and the front-wheel support mechanism 4 (orthe steering mobile section made up of the rear wheel 203 r and therear-wheel support mechanism 205) as well as the inertial force of thesteering mobile section which is generated when the steering mobilesection makes a motion relative to the vehicle body 2 (or vehicle body202).

A description will now be made, with reference to FIGS. 13 to 15, aboutdynamics models for a two-wheeled vehicle 1 having the mechanicalstructure similar to that of the front-wheel steering two-wheeledvehicle 1 shown in FIG. 1, for controlling the posture of the vehiclebody 2 by taking into account the inertial force of the steering mobilesection (hereinafter, referred to as “front-wheel steering mobilesection”) made up of the front wheel 3 f and the front-wheel supportmechanism 4, and the gravitational force acting on the front-wheelsteering mobile section.

FIG. 13 shows a two-wheeled vehicle 1 having the mechanical structuresimilar to that of the front-wheel steering two-wheeled vehicle 1 shownin FIG. 1. The two-wheeled vehicle 1 in FIG. 13 is different from thetwo-wheeled vehicle 1 in FIG. 1 in the manner of arrangement of the massand inertia moment which are set for modeling of the vehicle.

In the model of the two-wheeled vehicle 1 in FIG. 1, the mass of thefront-wheel steering mobile section is included in the vehicle body 2,and no mass point is set for the front-wheel steering mobile section. Incontrast, in the model of the two-wheeled vehicle 1 in FIG. 13, the massof the front-wheel steering mobile section is separated from the vehiclebody 2, and mass points are set respectively for the front-wheelsteering mobile section and the vehicle body 2.

More specifically, in the model of the two-wheeled vehicle 1 in FIG. 13,it is set such that the front-wheel steering mobile section has a masspoint 125 (hereinafter, referred to as “third mass point 125”) having amass m3. With a change in steering angle of the front wheel 3 f, thethird mass point 125 moves, together with the front-wheel steeringmobile section, relative to the vehicle body 2.

Further, in the model of the two-wheeled vehicle 1 in FIG. 13, a masspoint 126 having a mass mb, and an inertia moment Ib (inertia momentabout a longitudinal axis Crol which extends in the longitudinaldirection (X-axis direction) while passing through the mass point 126)are set for the vehicle body 2, as in the case of the two-wheeledvehicle 1 in FIG. 1.

In the model of the two-wheeled vehicle 1 in FIG. 13, however, the massm3 of the front-wheel steering mobile section is not included in thevehicle body 2. Therefore, the mass mb of the mass point 126 and itsposition, and the inertia moment Ib are different from the total mass mof the two-wheeled vehicle 1 in FIG. 1, the position of the overallcenter of gravity G (position of the mass point having the mass m), andthe inertia moment I, respectively.

Here, it is assumed that the arrangement of the mass and inertia momentof the two-wheeled vehicle 1 in FIG. 13 is equivalently transformed to amass point system which is made up of three mass points of a first masspoint 123 having a mass m1, a second mass point 124 having a mass m2,and a third mass point 125 having a mass m3, as shown in FIG. 14A.

The third mass point 125 is a mass point corresponding to thefront-wheel steering mobile section of the two-wheeled vehicle 1 in FIG.13. The height of the third mass point 125 is denoted as h3.

Of the two-wheeled vehicle 1 in FIG. 13, the portion excluding thefront-wheel steering mobile section (i.e. the portion having the masspoint 126 with the mass mb and the inertia moment Ib) is equivalentlytransformed to the first mass point 123 having the mass m1 and a heighth′ (=hb+c) and the second mass point 124 having the mass m2 and a height“0”, in a manner similar to that in which the two-wheeled vehicle 1 inFIG. 1 was equivalently transformed to the second model shown in FIG.2B.

In this case, the value of the difference c (=h′−hb) between h′ and hb(=height of the mass point 126 shown in FIG. 13) and the values of m1and m2 in FIG. 14A are determined by expressions which are obtained byreplacing I, m, and h on the right sides of the expressions (5b), (6b),and (7b) with Ib, mb, and hb, respectively.

It should be noted that since the first mass point 123 and the secondmass point 124 in the two-wheeled vehicle 1 in FIG. 13 are on the planeof symmetry of the vehicle body 2 of the two-wheeled vehicle 1 (plane ofsymmetry when the vehicle body 2 is considered to be bilaterallysymmetrical), as in the case of the two-wheeled vehicle 1 in FIG. 1, theinclination in the roll direction of the line segment connecting thefirst mass point 123 and the second mass point 124 corresponds to theinclination in the roll direction of the vehicle body 2 of thetwo-wheeled vehicle 1 in FIG. 13.

Now, consideration is given to equivalent transformation of the massarrangement in FIG. 14A to that in FIG. 14B. A second mass point 124 inFIG. 14B has its mass and position identical to those of the second masspoint 124 in FIG. 14A.

Further, a fifth mass point 128 in FIG. 14B is on the ground surface110. That is, the height of the fifth mass point 128 from the groundsurface 110 is “0”. A fourth mass point 127 has a height h4, which iskept constant.

First, it will be shown that a set of the first mass point 123 and thethird mass point 125 in FIG. 14A can be equivalently transformed to aset of the fourth mass point 127 and the fifth mass point 128 in FIG.14B.

This equivalent transformation can be performed to satisfy the followingsix conditions.

The first condition in the equivalent transformation is that the masssum of the set of the first mass point 123 and the third mass point 125agrees with the mass sum of the set of the fourth mass point 127 and thefifth mass point 128. This condition will be hereinafter referred to as“mass sum condition”.

The second condition in the equivalent transformation is that the heightof the center of gravity of the set of the first mass point 123 and thethird mass point 125 agrees with the height of the center of gravity ofthe set of the fourth mass point 127 and the fifth mass point 128. Thiscondition will be hereinafter referred to as “center-of-gravity heightcondition”.

The third condition in the equivalent transformation is that the inertiamoment about the origin of the set of the first mass point 123 and thethird mass point 125 agrees with the inertia moment about the origin ofthe set of the fourth mass point 127 and the fifth mass point 128. Thiscondition will be hereinafter referred to as “inertia moment condition”.

The fourth condition in the equivalent transformation is that theangular momentum about the origin of the set of the first mass point 123and the third mass point 125 agrees with the angular momentum about theorigin of the set of the fourth mass point 127 and the fifth mass point128. This condition will be hereinafter referred to as “angular momentumcondition”.

The fifth condition in the equivalent transformation is that in thebasic posture state of the front-wheel steering two-wheeled vehicle 1 inFIG. 13, the fourth mass point 127 and the fifth mass point 128 are onthe plane of symmetry of the vehicle body 2. That is, the fifthcondition is a condition that, in the aforesaid basic posture state, themovement amount in the Y-axis direction (position in the transversedirection) of each of the fourth mass point 127 and the fifth mass point128 is “0”. This condition will be hereinafter referred to as “base-timemovement amount condition”.

The sixth condition in the equivalent transformation is that the moment(gravitational moment) which is generated about the origin in thedirection about the X axis (roll direction) by the gravitational forceacting on the set of the first mass point 123 and the third mass point125 agrees with the moment (gravitational moment) which is generatedabout the origin in the direction about the X axis (roll direction) bythe gravitational force acting on the set of the fourth mass point 127and the fifth mass point 128. This condition will be hereinafterreferred to as “gravitational moment condition”.

The above-described six conditions of mass sum condition,center-of-gravity height condition, inertia moment condition, angularmomentum condition, base-time movement amount condition, andgravitational moment condition will be collectively called the “dynamicsconditions”. It should be noted that even in the case where thediscussion about the conditions is extended to a system having three ormore mass points, the conditions will be similarly called the mass sumcondition, center-of-gravity height condition, inertia moment condition,angular momentum condition, base-time movement amount condition,gravitational moment condition, and dynamics conditions.

Consideration is now given to determination of the relationalexpressions for determining a set of the movement amounts in the Y-axisdirection (positions in the transverse direction) of the fourth masspoint 127 and the fifth mass point 128 in accordance with a set of themovement amounts in the Y-axis direction (positions in the transversedirection) of the first mass point 123 and the third mass point 125, andalso determination of the height h4 (constant value) of the fourth masspoint 127, so as to satisfy the above-described dynamics conditions.

Here, xn (where n=1, 2, 3, 4, 5) is defined as the movement amount inthe Y-axis direction of the nth mass point.

According to the mass sum condition, center-of-gravity height condition,and inertia moment condition, the following expressions (101), (102),and (103), respectively, hold.

m1+m3=m4+m5  (101)

m1*h′+m3*h3=m4*h4  (102)

m1*h′*h′+m3*h3*h3=m4*h4*h4  (103)

From the above expressions (102) and (103), h4 and m4 are obtained asfollows.

h4=(m1*h′*h′+m3*h3*h3)/(m1*h′+m3*h3)  (104)

m4=(m1*h′+m3*h3)*(m1*h′+m3*h3)/(m1*h′*h′+m3*h3*h3)  (105)

From the expressions (101), (104), and (105), m5 is obtained as follows.

m5=m1*m3*(h′−h3)*(h′−h3)/(m1*h′*h′+m3*h3*h3)  (106)

In the above-described manner, the structural parameters h4, m4, and m5can be determined to satisfy the mass sum condition, center-of-gravityheight condition, and inertia moment condition. Hereinbelow, unknownvariables x4 and x5 will further be obtained.

In the state where the mass sum condition, center-of-gravity heightcondition, and inertia moment condition are satisfied, if the base-timemovement amount condition and angular momentum condition are alsosatisfied, then the integrated value of the angular momentum about theorigin of the set of the first mass point 123 and the third mass point125 will agree with the integrated value of the angular momentum aboutthe origin of the set of the fourth mass point 127 and the fifth masspoint 128. Accordingly, the following expression (107) holds.

m1*h′*x1+m3*h3*x3=m4*h4*x4  (107)

From the expressions (102) and (107), x4 is obtained as follows.

x4=(m1*h′*x1+m3*h3*×3)/(m1*h′+m3*h3)  (108)

On the other hand, according to the gravitational moment condition, thefollowing expression (109) holds.

m1*x1+m3*x3=m4*x4+m5*x5  (109)

From the expressions (108) and (109), x5 is obtained as follows.

x5=(m1*x1+m3*x3−m4*x4)/m5  (110)

Incidentally, x3 is determined uniquely from the roll angle φb of thevehicle body 2 and the steering angle δf of the front wheel 3 f. Thus,the function for determining x3 from the roll angle φb of the vehiclebody 2 and the steering angle δf of the front wheel 3 f is denoted asf3(φb, δf), and it is assumed that the following expression (111) holds.

x3=f3(φb,δf)  (111)

Although f3(φb, δf) may be determined experimentally, it may beexpressed analytically by using a trigonometric function, from thegeometric structure of the two-wheeled vehicle 1.

Further, in the case where φb is sufficiently small, sin(φb) can beapproximated by φb. Because of this and other reasons, f3(φb, δf) can beapproximated by the sum of a component attributable to φb and acomponent attributable to δf, as expressed by the following expression(112).

f3(φb,δf)=h3*φb+f33(δf)  (112)

Here, f33(δf) is a function which represents the component attributableto δf. When the divergence of the third mass point 125 from the steeringaxis Csf of the front wheel 3 f is denoted as bsf (with a positive valuerepresenting upward and forward divergence from the steering axis Csf ofthe front wheel 3 f) as shown in FIG. 13, f33(δf) is obtained as a sumof a component proportional to bsf*sin(δf) and a component proportionalto the height a. It should be noted that φb on the right side of theexpression (112) may be replaced with sin(φb).

Further, x1 is also determined uniquely from the roll angle φb of thevehicle body 2 and the steering angle δf the front wheel 3 f. Thus, thefunction for determining x1 from the roll angle φb of the vehicle body 2and the steering angle δf of the front wheel 3 f is denoted as f1(φb,δf), and it is assumed that the following expression (113) holds.

x1=f1(φb,δf)  (113)

Further, in the case where φb is sufficiently small, as in the case off3(φb, δf), f1(φb, δf) can be approximated by the sum of a componentattributable to φb and a component attributable to δf, as expressed bythe following expression (114).

f1(φb,δf)=h′*φb+f11(δf)  (114)

It should be noted that φb on the right side of the expression (114) maybe replaced with sin(φb).

From the expressions (104), (108), and (111) to (114), the followingexpression (115) is obtained.

x4=h4*φb+(m1*h′/(m1*h′+m3*h3))*f11(δf)+(m3*h3/(m1*h′+m3*h3))*f33(δf)  (115)

Here, a function f4(δf) is defined by the following expression (116).

f4(δf)=(m1*h′/(m1*h′+m3*h3))*f11(δf)+(m3*h3/(m1*h′+m3*h3))*f33(δf)  (116)

At this time, the expression (115) can be rewritten into the followingexpression (117).

x4=h4*φb+f4(δf)  (117)

It should be noted that φb on the right side of the expression (117) maybe replaced with sin(φb).

From the expressions (102), (110) to (114), and (117), the followingexpression (118) is obtained.

x5=(m1/m5)*f11(δf)+(m3/m5)*f33(δf)−(m4/m5)*f4(δf)  (118).

Therefore, x5 is expressed in the form shown by the following expression(119).

x5=f5(δf)  (119)

It should be noted that f5(δf) means the function (of δf) expressed bythe right side of the expression (118).

As described above, the set of the first mass point 123 and the thirdmass point 125 in FIG. 14A can be equivalently transformed to the set ofthe fourth mass point 127 and the fifth mass point 128 in FIG. 14B.Accordingly, the system (shown in FIG. 14A) made up of the first masspoint 123, the second mass point 124, and the third mass point 125 canbe equivalently transformed to the system (shown in FIG. 14B) made up ofthe fourth mass point 127, the second mass point 124, and the fifth masspoint 128.

Accordingly, in the case where the mass is set for the front-wheelsteering two-wheeled vehicle 1 in the manner as shown in FIG. 13, theapproximate dynamics model that approximately expresses the dynamics ofthe two-wheeled vehicle 1 in the aforesaid basic posture state andsimilar posture states (close to the basic posture state) can beequivalently transformed to the dynamics model of the system shown inFIG. 14B.

It should be noted that the position and the mass m2 of the second masspoint 124 in FIG. 14B are identical to those of the second mass point124 in FIG. 14A. The mass m2 of the second mass point 124 in FIGS. 14Aand 14B is generally different from that in the case of the front-wheelsteering two-wheeled vehicle 1 in which the mass has been set as shownin FIG. 1 (two-wheeled vehicle having no mass point for the front-wheelsteering mobile section).

The set of the second mass point 124 and the fifth mass point 128 inFIG. 14B can further be equivalently transformed to a sixth mass point129 having a mass m6, in accordance with the following expressions (120)and (121). The expression (120) shows the condition that the mass m6 ofthe sixth mass point 129 agrees with the sum of the masses m2 and m5 ofthe second mass point 124 and the fifth mass point 128, respectively.The expression (121) shows the condition that the position of the sixthmass point 129 coincides with the position of the center of gravity ofthe set of the second mass point 124 and the fifth mass point 128.

m6=m2+m5  (120)

x6=(m2/m6)*x2+(m5/m6)*x5  (121)

Accordingly, the dynamics model of the system shown in FIG. 14B can beequivalently transformed to the dynamics model of the system shown inFIG. 14C. The mass and position of the fourth mass point 127 in FIG. 14Care identical to those of the fourth mass point 127 in FIG. 14B.

On the other hand, x2 (which corresponds to the aforesaid q) isexpressed by a function of δf, as in the aforesaid expression (15), andx5 is expressed by a function of δf, f5(δf), as in the aforesaidexpression (119). Therefore, x6 is expressed as a function of δf, f(δf),as in the form in the following expression (122).

x6=f6(δf)  (122)

As with the mass point system (shown in FIG. 2B) corresponding to thetwo-wheeled vehicle 1 in FIG. 1 having no mass point set for thefront-wheel steering mobile section, the mass point system in FIG. 14Ccorresponding to the two-wheeled vehicle 1 in FIG. 13 having the masspoint 125 set for the front-wheel steering mobile section is made up ofa mass point (fourth mass point 127) which moves in accordance with theinclination in the roll direction of the vehicle body 2 and the steeringangle of the front wheel 3 f, and a mass point (sixth mass point 129)which moves on the ground surface 110 in accordance with the steeringangle of the front wheel 3 f, independently of the inclination in theroll direction of the vehicle body 2.

In this case, it can be considered that the fourth mass point 127corresponds to the first mass point (inverted pendulum mass point) 123in FIG. 2B and the sixth mass point 129 corresponds to the second masspoint 124 in FIG. 2B.

Therefore, the dynamic behavior of the two-wheeled vehicle 1 in FIG. 13,in which the mass point 125 has been set for the front-wheel steeringmobile section, can be expressed by the dynamics of the same form asthat of the dynamics model shown in FIG. 6, as in the case of thetwo-wheeled vehicle 1 in FIG. 1 having no mass point set for thefront-wheel steering mobile section.

The dynamic behavior of a two-wheeled vehicle 1 having a plurality ofmass points set for the front-wheel steering mobile section (forexample, a two-wheeled vehicle 1, as illustrated in FIG. 15, having amass point with a mass m7 and a mass point with a mass m8 set for thefront-wheel steering mobile section) can also be equivalentlytransformed to the behavior expressed by the dynamics model shown inFIG. 6.

Specifically, first, the dynamic behavior of the system composed of oneof the plurality of mass points of the front-wheel steering mobilesection and the mass point and inertia moment (inertia) of the vehiclebody 2 is equivalently transformed to the behavior of the dynamics modelshown in FIG. 6. Next, the dynamic behavior of the system obtained bycombining another one of the remaining mass points of the front-wheelsteering mobile section with the above, equivalently transformed systemis again equivalently transformed to the behavior of the dynamics modelshown in FIG. 6.

Thereafter, the similar procedure is repeated until all the mass pointsof the front-wheel steering mobile section are combined into the system.According to the above-described procedure, the dynamic behavior of atwo-wheeled vehicle 1 having a plurality of mass points set for thefront-wheel steering mobile section can also be equivalently transformedto the dynamic behavior of the system made up of a mass point (invertedpendulum mass point) which moves in accordance with the inclinationangle in the roll direction of the vehicle body 2 and the steering angleof the front wheel 3 f, and a mass point which moves on the groundsurface 110 in accordance with the steering angle of the front wheel 3f, independently of the inclination angle in the roll direction of thevehicle body 2.

Accordingly, the dynamic behavior of the two-wheeled vehicle 1 having amass point set for the front-wheel steering mobile section can beexpressed by the dynamics of the same form as that of the dynamics modelshown in FIG. 6.

Furthermore, in the case of a two-wheeled vehicle 1 in which a masspoint and an inertia moment about the mass point have been set for thefront-wheel steering mobile section, the system having the mass pointand the inertia moment can be equivalently transformed to a system madeup of a plurality of mass points. For example, in a similar manner as inthe case shown in FIG. 2A, two mass points each having half the mass ofthe mass point that has been set for the front-wheel steering mobilesection (hereinafter, referred to as “original mass point”) may bearranged at positions above and below the original mass point each at adistance of the radius of inertia therefrom. In this manner, the systemhaving the original mass point and the inertia moment about the originalmass point can be equivalently transformed to the system having aplurality of mass points set for the front-wheel steering mobilesection.

Accordingly, the dynamic behavior of a two-wheeled vehicle 1 in which amass point (original mass point) and an inertia moment about the masspoint have been set for the front-wheel steering mobile section can alsobe equivalently transformed to the dynamic behavior of a system which ismade up of a mass point (inverted pendulum mass point) which moves inaccordance with the inclination angle in the roll direction of thevehicle body 2 and the steering angle of the front wheel 3 f, and a masspoint which moves on the ground surface 110 in accordance with thesteering angle of the front wheel 3 f, independently of the inclinationangle in the roll direction of the vehicle body 2. Its dynamic behaviorcan be expressed by the dynamics of the same form as that of thedynamics model shown in FIG. 6.

The matters explained above can be summarized as follows. Even in thecase where at least one of a mass point and an inertia moment is set forthe steering mobile section (front-wheel steering mobile section) madeup of the front wheel 3 f and the front-wheel support mechanism 4, it ispossible to equivalently transform the dynamic behavior of thetwo-wheeled vehicle 1 to the behavior of a system which is made up of amass point that moves in accordance with the inclination angle in theroll direction of the vehicle body 2 and the steering angle of the frontwheel 3 f, and a mass point that moves on the ground surface 110 inaccordance with the steering angle of the front wheel 3 f, independentlyof the inclination angle in the roll direction of the vehicle body 2.

Accordingly, the dynamic behavior of the two-wheeled vehicle 1 having atleast one of the mass point and the inertia moment set for thefront-wheel steering mobile section can also be expressed by thedynamics of the same form as that of the dynamics model shown in FIG. 6.

That is, irrespective of whether at least one of the mass point and theinertia moment has been set for the front-wheel steering mobile sectionor neither of them has been set therefor, the dynamic behavior of thetwo-wheeled vehicle 1 can be equivalently transformed to the dynamicbehavior of a system which is made up of a mass point (inverted pendulummass point; hereinafter, this mass point may be generically referred toas “mass point A”) that moves in accordance with the inclination anglein the roll direction of the vehicle body 2 and the steering angle ofthe front wheel 3 f (steering control wheel), and a mass point(hereinafter, this mass point may be generically referred to as “masspoint B”) that moves on the ground surface 110 in accordance with thesteering angle of the front wheel 3 f (steering control wheel),independently of the inclination angle in the roll direction of thevehicle body 2.

To be more specific, the dynamic behavior of this system is expressed bythe dynamic behavior of the system in which the aforesaid mass point A(inverted pendulum mass point) accelerates or decelerates in response tothe gravitational moment which is generated about the origin due to thegravitational force acting on the mass point A, the gravitational momentwhich is generated about the origin due to the gravitational forceacting on the aforesaid mass point B, and the road surface reactionforce moment which is generated about the origin by the movement of thecenter of contact pressure, COP. That is, it is expressed by thedynamics of the same form as that of the dynamics model shown in FIG. 6.

For example, the dynamic behavior in the case where one mass point hasbeen set for the front-wheel steering mobile section (in the case of thetwo-wheeled vehicle 1 shown in FIG. 13) can be expressed by a dynamicsmodel in which the first mass point 123 (inverted pendulum mass point123) having the mass m1 in FIG. 6 has been replaced with the fourth masspoint 127 having the mass m4 shown in FIG. 14C (this corresponds to theabove-described mass point A) and the second mass point 124 having themass m2 in FIG. 6 has been replaced with the sixth mass point 129 havingthe mass m6 shown in FIG. 14C (this corresponds to the above-describedmass point B).

In the case of the rear-wheel steering two-wheeled vehicle 201 havingthe structure shown in FIG. 11 as well, matters similar to those in thecase of the front-wheel steering two-wheeled vehicle 1 hold. Therefore,irrespective of whether at least one of a mass point and an inertiamoment has been set for the steering mobile section (hereinafter,referred to as “rear-wheel steering mobile section”) made up of the rearwheel 203 r and the rear-wheel support mechanism 205, or neither of themhas been set therefor, the dynamic behavior of the two-wheeled vehicle201 can be equivalently transformed to the dynamic behavior of thesystem which is made up of the mass point A (inverted pendulum masspoint) that moves in accordance with the inclination angle in the rolldirection of the vehicle body 202 and the steering angle of the rearwheel 203 r (steering control wheel), and the mass point B that moves onthe ground surface 110 in accordance with the steering angle of the rearwheel 203 r (steering control wheel), independently of the inclinationangle in the roll direction of the vehicle body 202.

The dynamic behavior of this system is expressed by the dynamic behaviorof the system in which the aforesaid mass point A accelerates ordecelerates in response to the gravitational moment which is generatedabout the origin due to the gravitational force acting on the mass pointA, the gravitational moment which is generated about the origin due tothe gravitational force acting on the aforesaid mass point B, and theroad surface reaction force moment which is generated about the originby the movement of the center of contact pressure, COP. That is, it isexpressed by the dynamics of the same form as that of the dynamics modelshown in FIG. 6.

In summary of the foregoing, in each of the case where neither the masspoint nor the inertia moment has been set for the front-wheel (orrear-wheel) steering mobile section (hereinafter, this may be referredto as the “case of basic configuration”) and the case where one or bothof the mass point and the inertia moment have been set for thefront-wheel (or rear-wheel) steering mobile section (hereinafter, thismay be referred to as the “case of extended configuration”), the dynamicbehavior of the two-wheeled vehicle 1 (or the two-wheeled vehicle 201)becomes the behavior of the same form as that of the dynamics modelshown in FIG. 6 which corresponds to the case of basic configuration.

In the case of basic configuration, the inclination in the directionabout the X axis (roll direction) of the line segment connecting thefirst mass point 123 and the second mass point 124 corresponds to theinclination in the direction about the X axis (roll direction) of thevehicle body 2.

In contrast, in the case where one or both of the mass point and inertiamoment have been set for the front-wheel (or rear-wheel) steering mobilesection, the inclination in the direction about the X axis (rolldirection) of the line segment connecting the two mass points (theabove-described mass points A and B) does not necessarily correspond tothe inclination in the direction about the X axis (roll direction) ofthe vehicle body 2.

For the movement amount of the mass point A (inverted pendulum masspoint), however, the relationship as in the form obtained by extendingthe aforesaid expression (117) holds. Specifically, the movement amount(for example, dimensional quantity of the position (in the Y-axisdirection) or the angle (in the direction about the X axis)) of the masspoint A can be obtained by a sum of: a value proportional to theinclination angle φb in the direction about the X axis (roll direction)of the vehicle body 2 or its sine value sin(φb) (a value of a constantmultiple of φb or sin(φb)), and a value of a prescribed nonlinearfunction related to one or both of the steering angles δf and δr.

The above nonlinear function is a function related to the steering angleδf or δr (a function in the form of f(δf) or f(δr)) when the steeringcontrol wheel is a front wheel alone or a rear wheel alone,respectively. When the front and rear wheels are both steerable, thenonlinear function is a function related to both the steering angles δfand δr (for example, a function in the form of fa(δf, δr), or a functionin the form of fb(δf)+fc(δr)).

That is, the movement amount of the above-described mass point A can beobtained by a prescribed function related to the inclination angle φb inthe direction about the X axis (roll direction) of the vehicle body 2and one or both of the steering angles δf and δr (a function in the formof f(φb, δf, δr), or f(φb, δf), or f(φb, δr)).

Alternatively, the movement amount of the mass point A can be obtainedby a function into which the inclination angle φb in the direction aboutthe X axis (roll direction) of the vehicle body 2, a prescribed function(in the form of f(δf)) related to the steering angle δf, and aprescribed function (in the form of f(δr)) related to the steering angleδr are combined (for example, a function as a linear combination of φb,f(δf), and f(δr)).

It should be noted that in the case where the steering control wheel isthe front wheel or the rear wheel alone, the movement amount (in theY-axis direction) of the mass point B on the ground surface 110 can beobtained by a function (in the form of f(δf) or f(δr)) related to thesteering angle δf or δr, respectively. In the case where the front wheeland the rear wheel are both steerable, the movement amount (in theY-axis direction) of the mass point B on the ground surface 110 can beobtained by a function (in the form of f(δf, δr)) related to both thesteering angles δf and δr.

Further, as explained above, in either the case of basic configurationor the case of extended configuration, the dynamic behavior of thetwo-wheeled vehicle 1 (or the two-wheeled vehicle 201) becomes thebehavior of the same form as that of the dynamics model shown in FIG. 6corresponding to the case of basic configuration. Therefore, a similarargument as that about the dynamics model shown in FIG. 6 can bedeveloped about the control of the posture of the vehicle 2 (or 202).

That is, the dynamic matters similar to those in the case of basicconfiguration hold in the case of extended configuration as well. In thecase of extended configuration, however, the expressions related toMsum, M2, Mp, a_sum, a_p, and a_s for the front-wheel steeringtwo-wheeled vehicle 1 and Msum′, M2′, Mp′, a_sum′, a_p′, and a_s′ forthe rear-wheel steering two-wheeled vehicle 201 become more complicatedcompared to the expressions in the case of basic configuration.

In an ordinary two-wheeled vehicle having a conventional structure,however, the differences between the values obtained by theseexpressions in the case of extended configuration and those in the caseof basic configuration are small. More specifically, the values obtainedby the expressions for a_sum, a_p, a_s, a_sum′, a_p′, and a_s′ in thecase of extended configuration tend to be slightly lower (downside) thanthose in the case of basic configuration.

Therefore, in the case of extended configuration, the conditionsregarding the height a defined as explained above (the conditions forstably controlling the posture of the vehicle body 2 or 202) becomeslightly severer than in the case of basic configuration. That is, theconditions calculated regarding the height a in the case of extendedconfiguration become slightly severer than those calculated in the caseof basic configuration. Therefore, the conditions calculated regardingthe height a in the case of basic configuration become the prerequisitesfor favorably controlling the posture of the vehicle body 2 (or 202) ofthe two-wheeled vehicle 1 (or 201).

Supplementally, in a two-wheeled vehicle having both the front-wheelsteering mobile section and the rear-wheel steering mobile section (forexample, the two-wheeled vehicle 201 having the structure shown in FIG.11), in the case where at least one of a mass point and an inertiamoment has been set for each of the front-wheel steering mobile sectionand the rear-wheel steering mobile section, the system having the masspoint and the inertia moment for the entirety of the front-wheelsteering mobile section, the rear-wheel steering mobile section, and thevehicle body may be equivalently transformed to a system made up of twomass points (mass points A and B), in a similar manner as that describedabove in conjunction with the case where a plurality of mass points havebeen set for the front-wheel steering mobile section or the case where amass point and an inertia moment have been set for the front-wheelsteering mobile section.

In this case, the movement amount (for example, dimensional quantity ofthe position (in the Y-axis direction) or the angle (in the directionabout the X axis)) of the above-described mass point A can be obtainedby a sum of: a value proportional to the inclination angle φb in thedirection about the X axis (roll direction) of the vehicle body or itssine value sin(φb) (a value of a constant multiple of φb or sin(φb)),and a value of a prescribed nonlinear function related to both of thesteering angles δf and δr.

That is, the movement amount of the mass point A can be obtained by theinclination angle φb in the direction about the X axis (roll direction)of the vehicle body and a prescribed nonlinear function related to bothof the steering angles δf and δr. Further, in this case, the movementamount of the above-described mass point B can be obtained by aprescribed function related to the steering angles δf and δr.

It should be noted that the movement amount of the mass point A can beobtained in the above-described manner even in the case where thefront-wheel steering mobile section or the rear-wheel steering mobilesection is not equipped with an actuator for steering. Further, in atwo-wheeled vehicle having both the front-wheel steering mobile sectionand the rear-wheel steering mobile section, even in the case where themass point and the inertia moment have not been set for one or both ofthe front-wheel steering mobile section and the rear-wheel steeringmobile section, the movement amount of the mass point A can be obtainedin the above-described manner.

The above has described the fundamental technical matters related to thepresent invention.

The present invention will be described below on the basis of the above.

A mobile vehicle according to the present invention is a mobile vehiclewhich has a vehicle body and a front wheel and a rear wheel arrangedspaced apart from each other in a longitudinal direction of the vehiclebody,

one of the front wheel and the rear wheel being a steering control wheelwhich can be steered about a steering axis tilted backward,

the mobile vehicle including:

a steering actuator which generates a steering force for steering thesteering control wheel; and

a control device which controls the steering actuator so as to stabilizea posture of the vehicle body in accordance with at least an observedvalue of an inclination angle in a roll direction of the vehicle body,wherein

in a case where a state in which the front wheel and the rear wheel ofthe mobile vehicle are both stationary in an upright posture in contactwith a ground surface and axle centerlines of the front wheel and therear wheel extend in parallel with each other in a direction orthogonalto the longitudinal direction of the vehicle body is defined as a basicposture state,

the height a, from the ground surface, of a point of intersection of thesteering axis of the steering control wheel and a virtual straight lineconnecting a ground contact point of the steering control wheel and thecenter of axle of the steering control wheel in the basic posture stateis set to satisfy the following first condition (a first aspect of theinvention).

First Condition:

in a system made up of a mass point A, which moves in a horizontaldirection above the ground surface, with which the mobile vehicle comesinto contact, in accordance with the inclination angle in the rolldirection of the vehicle body and the steering angle of the steeringcontrol wheel, and a mass point B, which moves horizontally on theground surface, with which the mobile vehicle comes into contact, inaccordance with the steering angle of the steering control wheel,independently of the inclination angle in the roll direction of thevehicle body, the system having a mass of the mass point A, a mass ofthe mass point B, a height of the mass point A from the ground surface,a relationship among an inclination angle in the roll direction of thevehicle body, a steering angle of the steering control wheel, and adisplacement of the mass point A, and a relationship between a steeringangle of the steering control wheel and a displacement of the mass pointB which are set to have dynamic characteristics equivalent to those ofdynamics of the mobile vehicle in the case where the steering controlwheel of the mobile vehicle being stationary on a prescribed origin inthe basic posture state is steered by a steering angle δ, the systembeing also configured such that the mass point A accelerates ordecelerates in response to a first gravitational moment, generated aboutthe origin due to a gravitational force acting on the mass point A, asecond gravitational moment, generated about the origin due to agravitational force acting on the mass point B, and a road surfacereaction force moment, acting about the origin due to a road surfacereaction force in the vertical direction which acts on the center ofcontact pressure of the front wheel and the rear wheel of the mobilevehicle as a whole, in the case where a steering angle of the steeringcontrol wheel at the time when the steering control wheel is steered tocause a front end of the steering control wheel to turn left as themobile vehicle in the basic posture state is seen from above is definedas a positive steering angle and in the case where a moment that causesthe vehicle body to lean to the right is defined as a positive moment,the following holds: Mp/δ>−M2/δ, where M2 denotes the secondgravitational moment generated by movement of the mass point B at thetime when the steering control wheel of the mobile vehicle beingstationary on the origin in the basic posture state is steeredinstantaneously by the steering angle δ, and Mp denotes the road surfacereaction force moment generated about the origin by movement of thecenter of contact pressure at the time when the steering control wheelof the mobile vehicle being stationary on the origin in the basisposture state is steered instantaneously by the steering angle δ.

It should be noted that in the first aspect of the invention, “tostabilize a posture of the vehicle body” means to generate a moment (inthe roll direction) which acts on the mobile vehicle to make the posturein the roll direction of the vehicle body converge to or approach adesired posture (for example, the posture in the aforesaid basic posturestate).

The desired posture of the vehicle body may be a posture other than thatin the basic posture state. For example, in the case where the mobilevehicle is provided with a steering handlebar for allowing a rider ofthe mobile vehicle to steer the steering control wheel, or in the casewhere the wheel different from the steering control wheel steerable bythe aforesaid steering actuator is a steering control wheel not equippedwith an actuator for steering, the desired posture may be the onedetermined in accordance with the force applied to the steeringhandlebar by the rider's manipulation or the manipulated variable of thesteering handlebar, or in accordance with the steering angle of thesteering control wheel not equipped with the actuator.

According to the first aspect of the invention, the aforesaid height a,which is determined by the arrangement of the steering axis of thesteering control wheel (relative to the steering control wheel), is setto satisfy the aforesaid first condition.

Here, of the moments in the roll direction acting on the mobile vehiclein accordance with the steering of the steering control wheel in thebasic posture state, the second gravitational moment M2 and the roadsurface reaction force moment Mp have dependency on the height a.Therefore, setting the height a as appropriate makes it possible tosatisfy the first condition that Mp/δ>−M2/δ.

According to the first aspect of the invention, the height a is set tosatisfy the first condition, as described above. Therefore, a sum moment(Mp+M2) of the second gravitational moment M2 and the road surfacereaction force moment Mp, i.e. the moment corresponding to the aforesaidposture controlling manipulation moment Msum, becomes a moment in thepositive direction in the case where the steering angle δ is a smallpositive steering angle, and it becomes a moment in the negativedirection in the case where the steering angle δ is a small negativesteering angle.

Further, the sum moment (Mp+M2) becomes a moment in the same directionas the road surface reaction force moment Mp, and this road surfacereaction force moment Mp contributes to the control of the posture ofthe vehicle body.

This situation is similar to the situation in one of FIGS. 8D and 9A to9D in the case where the mass points 123 and 124 in FIGS. 8A to 8D and9A to 9D explained above are regarded as the aforesaid mass points A andB, respectively.

Accordingly, controlling the steering actuator by the control device soas to stabilize the posture of the vehicle body in accordance with atleast the observed value of the inclination angle in the roll directionof the vehicle body ensures that when the posture of the vehicle bodydeviates from a desired posture (hereinafter, this may be referred to as“stable vehicle body posture”), the posture of the vehicle body can bestably restored to the desired, stable vehicle body posture by thesteering of the steering control wheel.

Therefore, according to the first aspect of the invention, it ispossible to enhance the stability of the posture of the vehicle body bysteering of the front wheel or the rear wheel which is the steeringcontrol wheel.

Supplementally, in the system having the aforesaid mass points A and B,in the case where the steering control wheel of the mobile vehicle beingstationary on the prescribed origin in the basic posture state isinstantaneously steered by a small steering angle δ, the position of themass point A will not have any direct term with respect to the steeringangle of the steering control wheel. Therefore, the mass point A can beregarded as a fixed point.

That is, the displacement of the mass point A at the instant when thesteering control wheel has been steered by a small steering angle δ ismaintained at “0”. Accordingly, the inclination angle in the rolldirection of the vehicle body at this instant is obtained bysubstituting “0” for the displacement of the mass point A in theaforesaid relationship among the inclination angle in the roll directionof the vehicle body, the steering angle of the steering control wheel,and the displacement of the mass point A.

Further, the posture angle (a set of the angle in the roll direction andthe angle in the yaw direction) of the steering control wheel isobtained on the basis of the inclination angle in the roll direction ofthe vehicle body and the small steering angle δ of the steering controlwheel at that instant. Furthermore, on the basis of this posture angle(the set of the angle in the roll angle direction and the angle in theyaw direction) of the steering control wheel, the position (in thelateral direction of the vehicle body) of the center of contact pressure(COP) of the mobile vehicle is obtained.

Lastly, by multiplying the position of the center of contact pressure(COP) by the vertical load (road surface reaction force in the verticaldirection) of the steering control wheel, it is possible to obtain theroad surface reaction force moment Mp which acts about the prescribedorigin due to the movement of the center of contact pressure, COP, atthe time when the steering control wheel of the mobile vehicle beingstationary on the prescribed origin in the basis posture state isinstantaneously steered by a small steering angle δ.

In the first aspect of the invention, in order to set the height a tosatisfy the aforesaid first condition, the height a may be set, forexample, as follows.

In the first aspect of the invention, to satisfy the first condition,the height a is set, for example, to be smaller than a first prescribedvalue a_sum determined by the following expression (A) (a second aspectof the invention).

a_sum=((h+(I/m)/h)/(Rg+(I/m)/h))×Rs  (A)

where

polarity of a: a>0 in the case where the point of intersection is abovethe ground surface, a<0 in the case where the point of intersection isbelow the ground surface;

I: inertia moment of the mobile vehicle;

m: mass of the mobile vehicle;

h: height of the center of gravity of the mobile vehicle from the groundsurface in the basic posture state of the mobile vehicle;

Rg=(Lr/(Lf+Lr))×Rf+(Lf/(Lf+Lr))×Rr;

Lf: longitudinal distance between the center of gravity of the mobilevehicle and the center of axle of the front wheel in the basic posturestate of the mobile vehicle;

Lr: longitudinal distance between the center of gravity of the mobilevehicle and the center of axle of the rear wheel in the basic posturestate of the mobile vehicle;

Rf: radius of curvature of a transverse cross-sectional shape of thefront wheel at a ground contact point of the front wheel in the basicposture state of the mobile vehicle;

Rr: radius of curvature of a transverse cross-sectional shape of therear wheel at a ground contact point of the rear wheel in the basicposture state of the mobile vehicle; and

Rs: one of the radii of curvature Rf and Rr that corresponds to thesteering control wheel.

In the second aspect of the invention, in the case where the steeringcontrol wheel of the mobile vehicle is the front wheel, Rs in theexpression (A) agrees with the radius of curvature Rf of the front wheel(i.e., Rs=Rf).

Therefore, in this case, the first prescribed value a_sum defined by theright side of the expression (A) agrees with a_sum in the aforesaidexpression (28) related to the above-described front-wheel steeringtwo-wheeled vehicle 1 shown in FIG. 1.

Further, in this case, the point of intersection in the second aspect ofthe invention corresponds to the intersection point Ef described abovein conjunction with the front-wheel steering two-wheeled vehicle 1 inFIG. 1. Accordingly, the height a of the point of intersection in thesecond aspect of the invention corresponds to the height of theintersection point Ef.

In the case where the steering control wheel of the mobile vehicle inthe second aspect of the invention is the rear wheel, Rs in theexpression (A) agrees with the radius of curvature Rr of the rear wheel(i.e., Rs=Rr).

Therefore, in this case, the first prescribed value a_sum defined by theexpression (A) agrees with a_sum′ in the aforesaid expression (28)′related to the above-described rear-wheel steering two-wheeled vehicle201 shown in FIG. 11.

Further, in this case, the point of intersection in the second aspect ofthe invention corresponds to the intersection point Er′ described abovein conjunction with the rear-wheel steering two-wheeled vehicle 201 inFIG. 11. Accordingly, the height a of the point of intersection in thesecond aspect of the invention corresponds to the height of theintersection point Er′.

Therefore, in the second aspect of the invention, the event that theheight a of the point of intersection is smaller than a_sum determinedby the above expression (A) corresponds to the event that the height aof the intersection point Ef is smaller than a_sum in the expression(28) in the front-wheel steering two-wheeled vehicle 1 in FIG. 1 in thecase where the steering control wheel is the front wheel, and alsocorresponds to the event that the height a′ of the intersection pointEr′ is smaller than a_sum′ in the expression (28)′ in the rear-wheelsteering two-wheeled vehicle 201 in FIG. 11 in the case where thesteering control wheel is the rear wheel.

Therefore, according to the second aspect of the invention, it ispossible to set the height a of the point of intersection to satisfy theaforesaid first condition. Consequently, in the case where the postureof the vehicle body deviates from the above-described stable vehiclebody posture, the posture of the vehicle body can be stably restored tothe stable vehicle body posture by the steering of the steering controlwheel.

In the first aspect of the invention, it is more preferable that theheight a is set to further satisfy the following second condition (athird aspect of the invention).

Second Condition:

Msum/δ>−M2/δ, where Msum denotes a sum moment of the secondgravitational moment M2 and the road surface reaction force moment Mp.

According to the third aspect of the invention, the absolute value ofthe second gravitational moment M2, which would likely cause anoscillation phenomenon in the control system, is kept at or below theabsolute value of the above-described sum moment Msum (=Mp+M2), i.e. themoment Msum corresponding to the aforesaid posture controllingmanipulation moment.

Accordingly, it is possible to enhance the stability of the posturecontrol of the vehicle body, while restricting the oscillationphenomenon in the control system.

In the third aspect of the invention, for setting the height a so as tosatisfy the above-described first and second conditions, the height amay be set, for example, as follows.

In the third aspect of the invention, to satisfy the first condition andthe second condition, the height a is set, for example, to be notgreater than a second prescribed value a_s determined by the followingexpression (B) (a fourth aspect of the invention).

a _(—) s=((h+(I/m)/h)/(Rg+2×(I/m)/h))×Rs  (B)

It should be noted that the polarity of a and the meanings of I, m, h,Rg, and Rs are identical to those in the second aspect of the invention.

In the fourth aspect of the invention, the event that the height a ofthe point of intersection becomes not greater than a_s determined by theabove expression (B) corresponds to the event that the height a of theintersection point Ef becomes not greater than a_s in the expression(40) in the front-wheel steering two-wheeled vehicle 1 in FIG. 1 in thecase where the steering control wheel is the front wheel, and alsocorresponds to the event that the height a′ of the intersection pointEr′ becomes not greater than a_s′ in the expression (40)′ in therear-wheel steering two-wheeled vehicle 201 in FIG. 11 in the case wherethe steering control wheel is the rear wheel.

Therefore, according to the fourth aspect of the invention, it ispossible to set the height a of the point of intersection to satisfy theaforesaid first and second conditions. Consequently, the stability ofthe posture control of the vehicle body can be enhanced appropriately,while restricting the oscillation phenomenon in the control system.

Further, the mobile vehicle of the present invention may be a mobilevehicle having a vehicle body and a front wheel and a rear wheelarranged spaced apart from each other in a longitudinal direction of thevehicle body,

one of the front wheel and the rear wheel being a steering control wheelwhich can be steered about a steering axis tilted backward,

the mobile vehicle including:

a steering actuator which generates a driving force for steering thesteering control wheel; and

a control device which controls the steering actuator so as to stabilizea posture of the vehicle body in accordance with at least an observedvalue of an inclination angle in a roll direction of the vehicle body,wherein

in the case where a state in which the front wheel and the rear wheel ofthe mobile vehicle are both stationary in an upright posture in contactwith a ground surface and axle centerlines of the front wheel and therear wheel extend in parallel with each other in a direction orthogonalto the longitudinal direction of the vehicle body is defined as a basicposture state and in the case where a radius of curvature of atransverse cross-sectional shape of the steering control wheel at aground contact point of the steering control wheel in the basic posturestate of the mobile vehicle is denoted as Rs,

the height a, from the ground surface, of a point of intersection of thesteering axis of the steering control wheel and a virtual straight lineconnecting the ground contact point of the steering control wheel andthe center of axle of the steering control wheel in the basic posturestate is set to be not higher than the radius of curvature Rs (a fifthaspect of the invention).

That is, as explained above, it can be considered in the front-wheelsteering two-wheeled vehicle 1 in FIG. 1 or the rear-wheel steeringtwo-wheeled vehicle 201 in FIG. 11 that it is practically impossiblethat the center-of-gravity height h becomes equal to or lower than Rgwhich is defined by the aforesaid expression (25a).

In this case, when the height a of the point of intersection is set tobe not higher than the aforesaid radius of curvature Rs, which is theradius of curvature of the transverse cross-sectional shape of thesteering control wheel at the ground contact point of the steeringcontrol wheel in the basic posture state, then the height a of the pointof intersection is eventually set to satisfy the first condition in thefirst aspect of the invention, as explained above.

Therefore, according to the fifth aspect of the invention, in the casewhere the posture of the vehicle body deviates from the stable vehiclebody posture, the posture of the vehicle body can be stably restored tothe stable vehicle body posture by the steering of the steering controlwheel, as in the first aspect of the invention.

Consequently, according to the fifth aspect of the invention, it ispossible to enhance the stability of the posture of the vehicle body bysteering of the front wheel or the rear wheel which is the steeringcontrol wheel.

In the fifth aspect of the invention, it is more preferable that theheight a is set to a level below the ground surface (a sixth aspect ofthe invention).

According to the sixth aspect of the invention, it is eventuallypossible to satisfy the second condition in the third aspect of theinvention.

Additionally, the sensitivity of the restoring force (moment) of theposture of the vehicle body to the aforesaid stable vehicle bodyposture, which can be generated by the change in steering angle of thesteering control wheel, can be enhanced.

Accordingly, it is suitably possible to enhance the stability of thecontrol of the posture of the vehicle body, while suppressing anoscillation phenomenon in the control system.

It should be noted that in the first through sixth aspects of theinvention, the processing of the steering control of the steeringcontrol wheel (control of the steering actuator) by the control devicemay not be the processing established on the premise of the aforesaiddynamics model having the mass points A and B.

The control device may adopt, by way of example, the followingconfiguration. The control device includes, for example, an actuatoroperational target determining section which determines an operationaltarget of the aforesaid steering actuator (desired steering angularacceleration etc.), in accordance with a deviation of an observed valueof the inclination angle in the roll direction of the vehicle body, or astate quantity estimated from the observed value (state quantity relatedto the posture in the roll direction of the vehicle body, such as themotional state quantity of the aforesaid mass point A), from a desiredvalue for stabilizing the posture of the vehicle body (desired valuecorresponding to the aforesaid stable vehicle body posture), so as tomake the deviation approach zero, by a feedback control law. The controldevice is configured to control the steering actuator in accordance withthe determined operational target.

Supplementally, in the present specification, the “observed value” of agiven state quantity related to the mobile vehicle (such as theinclination angle in the roll direction of the vehicle body) means adetected value or an estimate of the actual value of the state quantity.In this case, the “detected value” means an actual value of the statequantity which is detected by an appropriate sensor. The “estimate”means a value which is estimated from a detected value of at least onestate quantity having correlation with the state quantity, on the basisof the correlation, or it means a pseudo estimate which can beconsidered to coincide with, or almost coincide with, the actual valueof the state quantity.

For the “pseudo estimate”, for example in the case where it is expectedthat the actual value of the state quantity can adequately track adesired value of the state quantity, the desired value may be adopted asthe pseudo estimate of the actual value of the state quantity.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram schematically showing a two-wheeled vehicle(front-wheel steering two-wheeled vehicle) for illustrating thefundamental technical matters related to the present invention;

FIGS. 2A and 2B are diagrams each showing a mass point system model ofthe two-wheeled vehicle in FIG. 1;

FIG. 3 is a diagram showing a model related to the behavior of thetwo-wheeled vehicle in FIG. 1;

FIG. 4 is a diagram for illustrating the behavior of the model in FIG.3;

FIG. 5 is a graph for illustrating the behavior of the model in FIG. 3;

FIG. 6 is a diagram showing a model for illustrating a dynamic behaviorof the two-wheeled vehicle in FIG. 1;

FIG. 7 is a graph showing the behavioral characteristics of thetwo-wheeled vehicle in FIG. 1;

FIGS. 8A to 8D are diagrams for illustrating the behavioralcharacteristics of the two-wheeled vehicle in FIG. 1;

FIGS. 9A to 9D are diagrams for illustrating the behavioralcharacteristics of the two-wheeled vehicle in FIG. 1;

FIG. 10 is a graph showing the behavioral characteristics of thetwo-wheeled vehicle in FIG. 1;

FIG. 11 is a diagram schematically showing another two-wheeled vehicle(rear-wheel steering two-wheeled vehicle) for illustrating thefundamental technical matters related to the present invention;

FIG. 12 is a diagram showing a model related to the behavior of thetwo-wheeled vehicle in FIG. 11;

FIG. 13 is a diagram schematically showing a two-wheeled vehicle(front-wheel steering two-wheeled vehicle) for illustrating additionaltechnical matters related to the present invention;

FIGS. 14A to 14C are diagrams each showing a mass point system model ofthe two-wheeled vehicle in FIG. 13;

FIG. 15 is a diagram schematically showing a two-wheeled vehicle(front-wheel steering two-wheeled vehicle) for illustrating additionaltechnical matters related to the present invention;

FIG. 16 is a side view of a mobile vehicle (two-wheeled vehicle)according to a first embodiment of the present invention;

FIG. 17 is a block diagram showing the configuration related to thecontrol of the mobile vehicle according to the first embodiment;

FIG. 18 is a block diagram showing the major functions of the controldevice shown in FIG. 17;

FIG. 19 is a block diagram showing the processing performed by theestimated inverted pendulum mass point lateral movement amountcalculating section shown in FIG. 18;

FIG. 20 is a block diagram showing the processing performed by theestimated inverted pendulum mass point lateral velocity calculatingsection shown in FIG. 18;

FIG. 21 is a block diagram showing the processing performed by theestimated traveling speed calculating section shown in FIG. 18;

FIG. 22 is a block diagram showing a first example of the processingperformed by the control gain determining section shown in FIG. 18;

FIG. 23 is a block diagram showing a second example of the processingperformed by the control gain determining section shown in FIG. 18;

FIG. 24 is a block diagram showing a third example of the processingperformed by the control gain determining section shown in FIG. 18;

FIG. 25 is a block diagram showing the processing performed by thedesired front-wheel rotational transfer velocity determining sectionshown in FIG. 18;

FIG. 26 is a block diagram showing a first example of the processingperformed by the posture control arithmetic section shown in FIG. 18;

FIG. 27 is a block diagram showing a second example of the processingperformed by the posture control arithmetic section shown in FIG. 18;

FIG. 28 is a block diagram showing a first example of the processingperformed by the desired handlebar angle determining section shown inFIG. 18;

FIG. 29 is a block diagram showing a second example of the processingperformed by the desired handlebar angle determining section shown inFIG. 18;

FIG. 30 is a block diagram showing the processing performed by afront-wheel steering actuator control section included in the controldevice shown in FIG. 17;

FIG. 31 is a block diagram showing the processing performed by afront-wheel driving actuator control section included in the controldevice shown in FIG. 17;

FIG. 32 is a block diagram showing the processing performed by ahandlebar driving actuator control section included in the controldevice shown in FIG. 17;

FIG. 33 is a side view of a mobile vehicle (two-wheeled vehicle)according to a second embodiment of the present invention;

FIG. 34 is a block diagram showing the configuration related to thecontrol of the mobile vehicle according to the second embodiment;

FIG. 35 is a block diagram showing the major functions of the controldevice shown in FIG. 34;

FIG. 36 is a block diagram showing the processing performed by theestimated inverted pendulum mass point lateral movement amountcalculating section shown in FIG. 35;

FIG. 37 is a block diagram showing the processing performed by theestimated inverted pendulum mass point lateral velocity calculatingsection shown in FIG. 35;

FIG. 38 is a block diagram showing the processing performed by theestimated traveling speed calculating section shown in FIG. 35;

FIG. 39 is a block diagram showing a first example of the processingperformed by the control gain determining section shown in FIG. 35;

FIG. 40 is a block diagram showing a second example of the processingperformed by the control gain determining section shown in FIG. 35;

FIG. 41 is a block diagram showing a third example of the processingperformed by the control gain determining section shown in FIG. 35;

FIG. 42 is a block diagram showing the processing performed by thedesired rear-wheel rotational transfer velocity determining sectionshown in FIG. 35;

FIG. 43 is a block diagram showing an example of the processingperformed by the posture control arithmetic section shown in FIG. 35;

FIG. 44 is a block diagram showing the processing performed by arear-wheel steering actuator control section included in the controldevice shown in FIG. 34; and

FIG. 45 is a block diagram showing the processing performed by arear-wheel driving actuator control section included in the controldevice shown in FIG. 34.

DESCRIPTION OF THE PREFERRED EMBODIMENTS First Embodiment

A first embodiment of the present invention will be described below withreference to FIGS. 16 to 32.

Referring to FIG. 16, a mobile vehicle 1A according to the presentembodiment is a two-wheeled vehicle embodying the front-wheel steeringtwo-wheeled vehicle 1 shown in FIG. 1. In the description of the presentembodiment, for convenience sake, the components of the mobile vehicle1A having the same functions as those of the front-wheel steeringtwo-wheeled vehicle 1 shown in FIG. 1 will be denoted by the samereference signs as those used in FIG. 1.

This mobile vehicle 1A (hereinafter, referred to as “two-wheeled vehicle1A”) has a vehicle body 2, and a front wheel 3 f and a rear wheel 3 rarranged spaced apart from each other in the longitudinal direction ofthe vehicle body 2.

On the upper surface of the vehicle body 2, a seat 6 is provided for arider to sit astride.

At the front portion of the vehicle body 2, a front-wheel supportmechanism 4 for axially supporting the front wheel 3 f, a steeringhandlebar 7 for a rider who has sat on the seat 6 to hold, and actuators8 and 9 are mounted. The actuator 8 generates a driving force forsteering the front wheel 3 f. The actuator 9 generates a driving forcefor moving the steering handlebar 7 in conjunction with the steering ofthe front wheel 3 f.

The front-wheel support mechanism 4 is made up of a front fork whichincludes a suspension mechanism such as a damper, for example. Themechanical structure of the front-wheel support mechanism is similar tothat of a conventional motorcycle, for example. At one end of thisfront-wheel support mechanism 4 (at its end on the front side of thevehicle body 2), the front wheel 3 f is axially supported, via bearingsor the like, such that it can rotate about the axle centerline Cf(rotational axis of the front wheel 3 f) that extends in the directionorthogonal to the diameter direction of the front wheel 3 f (in thedirection perpendicular to the paper plane of FIG. 16).

In the present embodiment, an actuator 10 for rotatively driving thefront wheel 3 f about its axle centerline Cf is attached to the axle ofthe front wheel 3 f. The actuator 10 serves as a power engine whichgenerates a thrust force for the two-wheeled vehicle 1A. In the presentembodiment, this actuator 10 (hereinafter, also referred to as“front-wheel driving actuator 10”) is made up of an electric motor (witha speed reducer).

It should be noted that the actuator 10 may be made up of a hydraulicactuator, for example, instead of the electric motor. Alternatively, theactuator 10 may be made up of an internal combustion engine.Furthermore, the actuator 10 may be attached to the vehicle body 2 at aposition apart from the axle of the front wheel 3 f, and the actuator 10and the axle of the front wheel 3 f may be connected by an appropriatepower transmission device.

The front-wheel support mechanism 4 is mounted to the front portion ofthe vehicle body 2 such that the mechanism can rotate about a steeringaxis Csf which is tilted backward. This configuration makes the frontwheel 3 f serve as a steering control wheel which can be rotated, or,steered about the steering axis Csf together with the front-wheelsupport mechanism 4. As the steering axis Csf is tilted backward, thefront wheel 3 f has a positive caster angle θcf.

In this case, in the two-wheeled vehicle 1A of the present embodiment,the relative arrangement of the steering axis Csf and the front wheel 3f in the basic posture state of the vehicle is set, as shown in FIG. 16,such that an intersection point Ef of the steering axis Csf and astraight line connecting the center of the axle of the front wheel 3 fand the ground contact point thereof is located below a ground surface110 in the basic posture state. Accordingly, the height a of theintersection point Ef from the ground surface 110 takes a negativevalue.

It should be noted that the basic posture state of the two-wheeledvehicle 1A is, as with the basic posture state of the two-wheeledvehicle 1 in FIG. 1, the state where the front wheel 3 f and the rearwheel 3 r are both stationary in the upright posture in contact with theground surface 110 and the axle centerlines (centers of the rotationalaxes) Cf and Cr of the front wheel 3 f and the rear wheel 3 r extend inparallel with each other in the direction orthogonal to the longitudinaldirection of the vehicle body 2.

The aforesaid actuator 8 generates, as a driving force for performingthe steering of the front wheel 3 f, a rotative driving force to causethe front wheel 3 f to rotate about the steering axis Csf. In thepresent embodiment, this actuator 8 is made up of an electric motor(with a speed reducer). The actuator 8 (hereinafter, also referred to as“front-wheel steering actuator 8”) is connected to the front-wheelsupport mechanism 4 so as to apply the rotative driving force about thesteering axis Csf to the front-wheel support mechanism 4.

Accordingly, as the rotative driving force is applied from thefront-wheel steering actuator 8 to the front-wheel support mechanism 4,the front-wheel support mechanism 4 is rotatively driven about thesteering axis Csf together with the front wheel 3 f. As a result, thefront wheel 3 f is steered by the rotative driving force from thefront-wheel steering actuator 8.

It should be noted that the actuator 8 is not limited to the electricmotor; it may be made up, for example, of a hydraulic actuator.

The steering handlebar 7 is mounted to the front portion of the vehiclebody 2 such that the steering handlebar 7 can rotate about a handlebaraxis Ch which is parallel to the steering axis Csf of the front wheel 3f. Although not shown in detail in the figure, this steering handlebar 7is equipped with an accelerator grip, brake lever, turn signal switch,and so on, as with the handlebar of a conventional motorcycle.

The aforesaid actuator 9 generates, as a driving force for moving thesteering handlebar 7, a rotative driving force for causing the steeringhandlebar 7 to rotate about the handlebar axis Ch. In the presentembodiment, this actuator 9 is made up of an electric motor (with aspeed reducer). The actuator 9 (hereinafter, also referred to as“handlebar driving actuator 9”) is connected to the steering handlebar 7so as to apply the rotative driving force about the handlebar axis Ch tothe steering handlebar 7.

In the two-wheeled vehicle 1A of the present embodiment, as shown inFIG. 16, the handlebar axis Ch of the steering handlebar 7 is offsetfrom the steering axis Csf of the front wheel 3 f. Alternatively, thehandlebar axis Ch may be arranged concentrically with the steering axisCsf. Still alternatively, the handlebar axis Ch may be tilted withrespect to the steering axis Csf.

Further, the actuator 9 may be made up of a hydraulic actuator, forexample, instead of the electric motor.

At the rear portion of the vehicle body 2, a rear-wheel supportmechanism 5 for axially supporting the rear wheel 3 r in a rotatablemanner is mounted. The rear-wheel support mechanism 5 includes a swingarm 11, and a suspension mechanism 12 made up of a coil spring, damper,and so on. These mechanical structures are similar to those in therear-wheel support mechanism in a conventional motorcycle, for example.

At one end of the swing arm 11 (at its end on the rear side of thevehicle body 2), the rear wheel 3 r is axially supported, via bearingsor the like, such that it can rotate about the axle centerline Cr(center of the rotational axis of the rear wheel 3 r) that extends inthe direction orthogonal to the diameter direction of the rear wheel 3 r(in the direction perpendicular to the paper plane of FIG. 16). Itshould be noted that the rear wheel 3 r is a non-steering control wheel.

Besides the above-described mechanical configuration, the two-wheeledvehicle 1A includes, as shown in FIG. 17, a control device 15 whichcarries out control processing for controlling the operations of theaforesaid front-wheel steering actuator 8, handlebar driving actuator 9,and front-wheel driving actuator 10 (and, hence, controlling the postureof the vehicle body 2 and so on).

The two-wheeled vehicle 1A further includes, as sensors for detectingvarious kinds of state quantities necessary for the control processingin the control device 15, a vehicle-body inclination detector 16 fordetecting an inclination angle φb in the roll direction of the vehiclebody 2, a front-wheel steering angle detector 17 for detecting asteering angle δf (angle of rotation about the steering axis Csf) of thefront wheel 3 f, a handlebar angle detector 18 for detecting a handlebarangle δh which is the rotational angle (angle of rotation about thehandlebar axis Ch) of the steering handlebar 7, a handlebar torquedetector 19 for detecting a handlebar torque Th which is the torqueacting on the steering handlebar 7 about the handlebar axis Ch, afront-wheel rotational speed detector 20 for detecting a rotationalspeed (angular velocity) of the front wheel 3 f, a rear-wheel rotationalspeed detector 21 for detecting a rotational speed (angular velocity) ofthe rear wheel 3 r, and an accelerator manipulation detector 22 whichoutputs a detection signal corresponding to the accelerator manipulatedvariable which is the manipulated variable (rotational amount) of theaccelerator grip of the steering handlebar 7.

It should be noted that the steering angle δf of the front wheel 3 fmore specifically means the rotational angle of the front wheel 3 f fromthe steering angle (neutral steering angle) in its non-steered state(the state in which the direction of the axle centerline Cf of the frontwheel 3 f corresponds to the direction orthogonal to the longitudinaldirection of the vehicle body 2 (or, direction parallel to the Y axis)).Therefore, the steering angle δf of the front wheel 3 f in thenon-steered state is “0”. The positive rotational direction of thesteering angle δf of the front wheel 3 f corresponds to the direction ofrotation that makes the front end of the front wheel 3 f turn left withrespect to the vehicle body 2 (in other words, the direction in whichthe front wheel 3 f turns counterclockwise about the steering axis Csfas the two-wheeled vehicle 1A is seen from above), as in the case of thetwo-wheeled vehicle 1 shown in FIG. 1.

Further, the handlebar angle δh of the steering handlebar 7 means therotational angle of the steering handlebar 7 from its posture statecorresponding to the non-steered state of the front wheel 3 f. Thepositive rotational direction of the handlebar angle δh corresponds tothe direction in which the steering handlebar 7 turns counterclockwiseabout the handlebar axis Ch as the two-wheeled vehicle 1A is seen fromabove.

The control device 15, which is an electronic circuit unit made up of aCPU, RAM, ROM, interface circuit and so on, is mounted on the vehiclebody 2. This control device 15 is configured to receive outputs(detection signals) from the respective detectors 16 to 22 describedabove.

The control device 15 may include a plurality of CPUs or processors.Further, the control device 15 may be made up of a plurality of mutuallycommunicable electronic circuit units.

The vehicle-body inclination detector 16, which is made up of anacceleration sensor and a gyro sensor (angular velocity sensor), forexample, is mounted on the vehicle body 2. In this case, the controldevice 15 carries out arithmetic processing on the basis of the outputsof the acceleration sensor and the gyro sensor, to measure theinclination angle in the roll direction (more specifically, theinclination angle in the roll direction with respect to the verticaldirection (direction of gravitational force)) of the vehicle body 2. Forthis measurement, the technique proposed by the present applicant inJapanese Patent No. 4181113, for example, may be adopted.

The front-wheel steering angle detector 17 is made up, for example, of arotary encoder attached to the front-wheel steering actuator 8 (electricmotor) on the aforesaid steering axis Csf.

The handlebar angle detector 18 is made up, for example, of a rotaryencoder attached to the handlebar driving actuator 9 (electric motor) onthe aforesaid handlebar axis Ch.

The handlebar torque detector 19 is made up, for example, of a forcesensor interposed between the steering handlebar 7 and the handlebardriving actuator 9.

The front-wheel rotational speed detector 20 is made up, for example, ofa rotary encoder attached to the axle of the front wheel 3 f.

The rear-wheel rotational speed detector 21 is made up, for example, ofa rotary encoder attached to the axle of the rear wheel 3 r.

The accelerator manipulation detector 22 is made up, for example, of arotary encoder or a potentiometer built in the steering handlebar 7.

The functions of the above-described control device 15 will be describedfurther with reference to FIG. 18. The XYZ coordinate system used in thefollowing description is, as in the case of the two-wheeled vehicle 1 inFIG. 1, a coordinate system in which, in the basic posture state of thetwo-wheeled vehicle 1A, the vertical direction (up-and-down direction)is defined as the Z-axis direction, the longitudinal direction of thevehicle body 2 as the X-axis direction, the lateral direction of thevehicle body 2 as the Y-axis direction, and a point on the groundsurface 110 immediately beneath the overall center of gravity G of thetwo-wheeled vehicle 1A as the origin (see FIG. 16).

Further, in the following description, the suffix “_act” is added to thereference characters of a state quantity as a sign indicating an actualvalue or its observed value (detected value or estimate). For a desiredvalue, the suffix “_cmd” is added.

The control device 15 includes, as functions implemented when the CPUexecutes installed programs (functions implemented by software) or asfunctions implemented by hardware, as shown in FIG. 18: an estimatedinverted pendulum mass point lateral movement amount calculating section31 which calculates an estimate of an actual value Pb_diff_y_act(hereinafter, referred to as “estimated inverted pendulum mass pointlateral movement amount Pb_diff_y_act”) of an inverted pendulum masspoint lateral movement amount Pb_diff_y representing a movement amountin the Y-axis direction (lateral direction of the vehicle body 2) of aninverted pendulum mass point 123 (=first mass point 123) of thetwo-wheeled vehicle 1A, an estimated inverted pendulum mass pointlateral velocity calculating section 32 which calculates an estimate ofan actual value Vby_act (hereinafter, referred to as “estimated invertedpendulum mass point lateral velocity Vby_act”) of an inverted pendulummass point lateral velocity Vby representing a translational velocity inthe Y-axis direction (lateral direction of the vehicle body 2) of theinverted pendulum mass point 123, an estimated traveling speedcalculating section 33 which calculates an estimate of the actual valueVox_act (hereinafter, referred to as “estimated traveling speedVox_act”) of the traveling speed Vox of the two-wheeled vehicle 1A, adesired posture state determining section 34 which determines a desiredvalue Pb_diff_y_cmd (hereinafter, referred to as “desired invertedpendulum mass point lateral movement amount Pb_diff_y_cmd”) of theinverted pendulum mass point lateral movement amount Pb_diff_y and adesired value Vby_cmd (hereinafter, referred to as “desired invertedpendulum mass point lateral velocity Vby_cmd”) of the inverted pendulummass point lateral velocity Vby, a control gain determining section 35which determines values of a plurality of gains K1, K2, K3, K4, and Khfor posture control of the vehicle body 2, and a desired front-wheelrotational transfer velocity determining section 36 which determines adesired value Vf_cmd (hereinafter, referred to as “desired front-wheelrotational transfer velocity Vf_cmd”) of the rotational transfervelocity Vf of the front wheel 3 f (translational velocity of the frontwheel 3 f as the front wheel 3 f rolls on the ground surface 110).

The control device 15 further includes: a posture control arithmeticsection 37 which carries out arithmetic processing for the posturecontrol of the vehicle body 2 to thereby determine a desired valueδf_cmd (hereinafter, referred to as “desired front-wheel steering angleδf_cmd”) of the steering angle δf of the front wheel 3 f, a desiredvalue δf_dot_cmd (hereinafter, referred to as “desired front-wheelsteering angular velocity δf_dot_cmd”) of the steering angular velocityδf_dot which is a temporal change rate of the steering angle δf, and adesired value δf_dot2_cmd (hereinafter, referred to as “desiredfront-wheel steering angular acceleration δf_dot2_cmd”) of the steeringangular acceleration δf_dot2 which is a temporal change rate of thesteering angular velocity δf_dot, and a desired handlebar angledetermining section 38 which determines a desired value δh_cmd(hereinafter, referred to as “desired handlebar angle δh_cmd”) of thehandlebar angle δh of the steering handlebar 7, and a desired valueδh_dot_cmd (hereinafter, referred to as “desired handlebar angularvelocity δh_dot_cmd”) of the handlebar angular velocity δh_dot which isa temporal change rate of the handlebar angle δh.

The control device 15 carries out the processing in the above-describedfunctional sections successively at prescribed control processingcycles. The control device 15 then controls the front-wheel steeringactuator 8 in accordance with the desired front-wheel steering angleδf_cmd, the desired front-wheel steering angular velocity δf_dot_cmd,and the desired front-wheel steering angular acceleration δf_dot2_cmddetermined by the posture control arithmetic section 37.

Further, the control device 15 controls the front-wheel driving actuator10 in accordance with the desired front-wheel rotational transfervelocity Vf_cmd determined by the desired front-wheel rotationaltransfer velocity determining section 36.

Further, the control device 15 controls the handlebar driving actuator 9in accordance with the desired handlebar angle δh_cmd and the desiredhandlebar angular velocity δh_dot_cmd determined by the desiredhandlebar angle determining section 38.

The control processing performed by the control device 15 will bedescribed below in detail.

At each control processing cycle, the control device 15 first carriesout the processing in the estimated inverted pendulum mass point lateralmovement amount calculating section 31. It should be noted that thealgorithm of the processing in the estimated inverted pendulum masspoint lateral movement amount calculating section 31 in the presentembodiment has been established assuming, by way of example, that thedynamic behavior of the two-wheeled vehicle 1A is expressed by thedynamic behavior that is obtained when the system in which a mass pointand an inertia moment have been set only for the vehicle body 2 of thetwo-wheeled vehicle 1A, as in the two-wheeled vehicle 1 in FIG. 1, isequivalently transformed to the system, shown in FIG. 2B, which is madeup of the aforesaid first mass point 123 (inverted pendulum mass point)and the second mass point 124.

As shown in FIG. 18, the estimated inverted pendulum mass point lateralmovement amount calculating section 31 receives a detected value of theactual value φb_act (hereinafter, referred to as “detected roll angleφb_act”) of the roll angle (inclination angle in the direction about theX axis (roll direction))+φb of the vehicle body 2, and a detected valueof the actual value δf_act (hereinafter, referred to as “detectedfront-wheel steering angle δf_act”) of the steering angle δf of thefront wheel 3 f.

The detected roll angle φb_act is a detected value (observed value)indicated by an output from the vehicle-body inclination detector 16,and the detected front-wheel steering angle δf_act is a detected value(observed value) indicated by an output from the front-wheel steeringangle detector 17.

Here, in the case where it is assumed that a mass point and an inertiamoment are set only for the vehicle body 2 of the two-wheeled vehicle 1Aand that the dynamic behavior of the two-wheeled vehicle 1A is expressedby the behavior of the mass point system made up of the first mass point123 (inverted pendulum mass point) and the second mass point 124, thefirst mass point 123 and the second mass point 124 are on the plane ofsymmetry of the vehicle body 2 (plane of symmetry when the vehicle body2 is considered to be bilaterally symmetrical), as described above.Therefore, the inclination in the roll direction of the line segmentconnecting the first mass point 123 and the second mass point 124corresponds to the inclination in the roll direction of the vehicle body2 of the two-wheeled vehicle 1A.

Accordingly, in the case where the inclination angle φb in the rolldirection of the vehicle body 2 of the two-wheeled vehicle 1A issufficiently small, the difference between the movement amount in theY-axis direction of the first mass point 123 and the movement amount inthe Y-axis direction of the second mass point 124 coincides with a valueobtained by multiplying the inclination angle φb in the roll directionof the vehicle body 2 by the height h′ of the first mass point 123.

Further, in the two-wheeled vehicle 1A of the present embodiment, thefront wheel 3 f alone is a steering control wheel. Therefore, themovement amount q in the Y-axis direction of the second mass point 124is determined uniquely from the steering angle δf of the front wheel 3f, as explained above.

Accordingly, the movement amount in the Y-axis direction of the firstmass point 123, which is the inverted pendulum mass point, is obtainedas a sum of a component attributable to the inclination in the rolldirection of the vehicle body 2 of the two-wheeled vehicle 1A and acomponent attributable to the steering angle δf of the front wheel 3 f.

The estimated inverted pendulum mass point lateral movement amountcalculating section 31 uses this relationship to calculate the estimatedinverted pendulum mass point lateral movement amount Pb_diff_y_act onthe basis of the detected roll angle φb_act and the detected front-wheelsteering angle δf_act.

More specifically, the estimated inverted pendulum mass point lateralmovement amount calculating section 31 calculates the estimated invertedpendulum mass point lateral movement amount Pb_diff_y_act by theprocessing shown in the block diagram in FIG. 19.

This processing is configured to sum up a first estimatedlateral-movement amount component Pb_diff_y_act_(—)1, which is anestimate of the actual movement amount in the Y-axis direction of theinverted pendulum mass point 123 caused by the inclination in the rolldirection of the vehicle body 2, and a second estimated lateral movementamount component Pb_diff_y_act_(—)2, which is an estimate of the actualmovement amount in the Y-axis direction of the inverted pendulum masspoint 123 caused by the steering of the front wheel 3 f, to therebycalculate the estimated inverted pendulum mass point lateral movementamount Pb_diff_y_act.

In FIG. 19, a processing section 31-1 represents a processing sectionwhich obtains the first estimated lateral movement amount componentPb_diff_y_act_(—)1, a processing section 31-2 represents a processingsection which obtains the second estimated lateral movement amountcomponent Pb_diff_y_act_(—)2, and a processing section 31-3 represents aprocessing section which sums up the first estimated lateral movementamount component Pb_diff_y_act_(—)1 and the second estimated lateralmovement amount component Pb_diff_y_act_(—)2.

The processing section 31-1 determines the first estimated lateralmovement amount component Pb_diff_y_act_(—)1 in accordance with thedetected roll angle φb_act at the current time. More specifically, theprocessing section 31-1 multiplies the detected roll angle φb_act (anglevalue in [rad]) by the height h′(=c+h), multiplied by −1, of theinverted pendulum mass point 123, to calculate the first estimatedlateral movement amount component Pb_diff_y_act_(—)1 (=φb_act*(−h′)).

Accordingly, the first estimated lateral movement amount componentPb_diff_y_act_(—)1 is calculated, in accordance with the detected rollangle φb_act, as a value of a linear function with respect to the rollangle φb of the vehicle body 2 (a value of a constant multiple of φb).Further, Pb_diff_y_act_(—)1 becomes zero in the state where φb_act=0(where the vehicle body 2 is not leaned to the right or left), andtherefore, it is the movement amount in the Y-axis direction withreference to the position of the inverted pendulum mass point 123 inthat state.

It should be noted that sin(φb_act) is approximated by φb_act in thecalculating processing in the processing section 31-1. Further, thevalue of h′ (or c, h) has been preset in the two-wheeled vehicle 1A andis stored in a memory in the control device 15. For example, the valuehas been set to satisfy the relationship in the aforesaid expression(5b) (the relationship that c(=h′−h)=I/(m*h)), from the height h of theoverall center of gravity G in the basic posture state of thetwo-wheeled vehicle 1A, the overall inertia I of the two-wheeled vehicle1A (inertia moment about the axis passing through the overall center ofgravity G and parallel to the X-axis direction), and the total mass m ofthe two-wheeled vehicle 1A.

The value of h′, however, may be set to a value roughly approximatingthe value satisfying the relationship in the above expression (5b) suchthat optimal control characteristics can be obtained on the basis ofvarious experiments, simulation, etc.

The processing section 31-2 in FIG. 19 determines the second estimatedlateral movement amount component Pb_diff_y_act_(—)2 in accordance withthe detected front-wheel steering angle of act at the current time. Morespecifically, the processing section 31-2 obtains the second estimatedlateral movement amount component Pb_diff_y_act_(—)2 (=Plfy(δf_act))from the detected front-wheel steering angle δf_act at the current time,by a preset conversion function Plfy(δf). That is, the processingsection 31-2 obtains a value Plfy(δf_act) of the conversion functionPlfy(δf) corresponding to δf_act, and determines the obtained value asthe second estimated lateral movement amount componentPb_diff_y_act_(—)2.

The above conversion function Plfy(δf) is defined, for example, by amapping or an arithmetic expression. The conversion function Plfy(δf) isa nonlinear function which has been preset, as illustrated by the graphshown in the processing section 31-2 in FIG. 19, such that itmonotonically changes (in the present embodiment, monotonicallydecreases) with increasing steering angle δf the front wheel 3 f, andsuch that the magnitude of the rate of change of Plfy(δf) with respectto the steering angle δf (the amount of change of Plfy(δf) per unitincrease δf) becomes relatively small in the region where the magnitude(absolute value) of the steering angle δf the front wheel 3 f isrelatively large, compared to that in the region where the magnitude ofthe steering angle δf is small (region where δf is near zero).

Accordingly, the second estimated lateral movement amount componentPb_diff_y_act_(—)2 is determined, in accordance with the detectedfront-wheel steering angle δf_act, as a value of a nonlinear functionwith respect to the steering angle δf the front wheel 3 f.

The estimated inverted pendulum mass point lateral movement amountcalculating section 31 determines the estimated inverted pendulum masspoint lateral movement amount Pb_diff_y_act by summing up, in theprocessing section 31-3, the first estimated lateral movement amountcomponent Pb_diff_y_act_(—)1 and the second estimated lateral movementamount component Pb_diff_y_act_(—)2 calculated in the above-describedmanner.

Accordingly, the estimated inverted pendulum mass point lateral movementamount Pb_diff_y_act is determined by the following expression (51).

$\begin{matrix}\begin{matrix}{{{Pb\_ diff}{\_ y}{\_ act}} = {{{Pb\_ diff}{\_ y}{\_ act}\_ 1} + {{Pb\_ diff}{\_ y}{\_ act}\_ 2}}} \\{= {{{\Phi b\_ act}*\left( {- h^{\prime}} \right)} + {{Plfy}({\delta f\_ act})}}}\end{matrix} & (51)\end{matrix}$

In the above expression (51), the first term on the right side is alinear term with respect to the detected roll angle φb_act, and thesecond term on the right side is a nonlinear term with respect to thedetected front-wheel steering angle δf_act.

It should be noted that the second term on the right side of theexpression (51) can be ignored when the magnitude of the valuePlfy(δf_act) of the aforesaid conversion function Plfy(δf) correspondingto the actual steering angle δf_act of the front wheel 3 f issufficiently small (when the magnitude of δf_act is small). In thiscase, the detected roll angle φb_act of the vehicle body 2 may be usedinstead of the estimated inverted pendulum mass point lateral movementamount Pb_diff_y_act.

With this configuration, the processing in the estimated invertedpendulum mass point lateral movement amount calculating section 31becomes unnecessary, and the computational load of the control device 15can be reduced.

Next, the control device 15 carries out the processing in the estimatedinverted pendulum mass point lateral velocity calculating section 32.

As shown in FIG. 18, the estimated inverted pendulum mass point lateralvelocity calculating section 32 receives the estimated inverted pendulummass point lateral movement amount Pb_diff_y_act calculated in theestimated inverted pendulum mass point lateral movement amountcalculating section 31, a detected front-wheel steering angle δf_act,and an estimate of the actual value Vf_act (hereinafter, referred to as“estimated front-wheel rotational transfer velocity Vf_act”) of therotational transfer velocity Vf of the front wheel 3 f.

It should be noted that the estimated front-wheel rotational transfervelocity Vf_act is a velocity which is calculated by multiplying adetected value (observed value) of the rotational angular velocity ofthe front wheel 3 f, indicated by an output from the aforesaidfront-wheel rotational speed detector 20, by a predetermined effectiverolling radius of the front wheel 3 f.

The estimated inverted pendulum mass point lateral velocity calculatingsection 32 carries out the processing shown in the block diagram in FIG.20 to calculate an estimated inverted pendulum mass point lateralvelocity Vby_act.

This processing is configured to sum up a first estimated lateralvelocity component Vby_act_(—)1, which is an estimate of the actualtransfer velocity (relative to the origin) in the Y-axis direction ofthe inverted pendulum mass point 123 as seen from the origin of the XYZcoordinate system set in the above-described manner for the two-wheeledvehicle 1A, and a second estimated lateral velocity componentVby_act_(—)2, which is an estimate of the actual transfer velocity inthe Y-axis direction of the inverted pendulum mass point 123 (=transfervelocity of the origin of the XYZ coordinate system) caused by thetranslational movement of the two-wheeled vehicle 1A accompanying therolling of the front wheel 3 f while the front wheel 3 f is beingsteered (when the actual steering angle of the front wheel 3 f is not“0”), to thereby calculate the estimated inverted pendulum mass pointlateral velocity Vby_act.

In FIG. 20, a processing section 32-1 represents a processing sectionwhich obtains the first estimated lateral velocity componentVby_act_(—)1, a processing section 32-2 represents a processing sectionwhich obtains the second estimated lateral velocity componentVby_act_(—)2, and a processing section 32-3 represents a processingsection which sums up the first estimated lateral velocity componentVby_act_(—)1 and the second estimated lateral velocity componentVby_act_(—)2.

The processing section 32-1 calculates, as the first estimated lateralvelocity component Vby_act_(—)1, a temporal change ratePb_diff_y_dot_act (amount of change per unit time) at the current timeof the estimated inverted pendulum mass point lateral movement amountPb_diff_y_act successively calculated by the estimated inverted pendulummass point lateral movement amount calculating section 31. That is, theprocessing section 32-1 calculates a differential valuePb_diff_y_dot_act of Pb_diff_y_act as Vby_act_(—)1.

Further, the processing section 32-2 multiplies, in a processing section32-2-1, a detected front-wheel steering angle δf_act at the current timeby a cosine value cos(θcf) of the caster angle θcf of the front wheel 3f, to thereby calculate an estimate of the actual value δ′f_act(hereinafter, referred to as “estimated front-wheel effective steeringangle δ′f_act”) of a front-wheel effective steering angle δ′f whichcorresponds to the rotational angle in the yaw direction of the frontwheel 3 f.

Supplementally, the front-wheel effective steering angle δ′f is an angleof the line of intersection of the ground surface 110 and the rotationalplane of the front wheel 3 f being steered (plane passing through thecenter of the axle of the front wheel 3 f and orthogonal to the axlecenterline Cf of the front wheel 3 f) with respect to the longitudinaldirection (X-axis direction) of the vehicle body 2.

In the case where the roll angle φb of the vehicle body 2 is relativelysmall, the estimated front-wheel effective steering angle δ′f_act can becalculated approximately by the following expression (52). Theprocessing in the above-described processing section 32-2-1 is theprocess of approximately calculating δ′f_act by the expression (52).

δ′f_act=cos(θcf)*δf_act  (52)

To further improve the accuracy of δ′f_act, δ′f_act may be obtained by amapping from δf_act. Alternatively, to still further improve theaccuracy of δ′f_act, δ′f_act may be obtained by a mapping(two-dimensional mapping) or the like from δf_act and a detected rollangle φb_act.

The processing section 32-2 further calculates a sine value sin(δ′f_act)of the calculated, estimated front-wheel effective steering angleδ′f_act and multiplies the estimated front-wheel rotational transfervelocity Vf_act at the current time by the sine value, in a processingsection 32-2-2 and a processing section 32-2-3, to thereby calculate atransfer velocity in the Y-axis direction (in other words, a componentin the Y-axis direction of Vf_act) of the ground contact part of thefront wheel 3 f.

Further, the processing section 32-2 multiplies, in a processing section32-2-4, the value as a result of calculation in the processing section32-2-3 by Lr/L (where L=Lf+Lr), to obtain a second estimated lateralvelocity component Vby_act_(—)2 (=Vf_act*sin(δf_act)*(Lr/L)).

It should be noted that the above-described Lr and Lf in this processinghave the same meanings as those in the two-wheeled vehicle 1 in FIG. 1.That is, Lr refers to a distance in the X-axis direction between theground contact point of the rear wheel 3 r and the overall center ofgravity G in the basic posture state of the two-wheeled vehicle 1A, andLf refers to a distance in the X-axis direction between the groundcontact point of the front wheel 3 f and the overall center of gravity Gin the basic posture state of the two-wheeled vehicle 1A.

The values of Lr and Lf have been preset for the two-wheeled vehicle 1Aand are stored in a memory in the control device 15.

The value of the caster angle θcf used in the processing in theprocessing section 32-2 has also been preset for the two-wheeled vehicle1A, as with the values of Lf and Lr, and is stored in the memory in thecontrol device 15.

The estimated inverted pendulum mass point lateral velocity calculatingsection 32 sums up, in the processing section 32-3, the first estimatedlateral velocity component Vby_act_(—)1 and the second estimated lateralvelocity component Vby_act_(—)2 calculated in the above-describedmanner, to calculate an estimated inverted pendulum mass point lateralvelocity Vby_act.

Accordingly, the estimated inverted pendulum mass point lateral velocityVby_act is calculated by the following expression (53).

$\begin{matrix}\begin{matrix}{{Vby\_ act} = {{{Vby\_ act}\_ 1} + {{Vby\_ act}\_ 2}}} \\{= {{{Pb\_ diff}{\_ y}{\_ dot}{\_ act}} + {{Vf\_ act}*{\sin \left( {\delta^{\prime}{f\_ act}} \right)}*\left( {{Lr}/L} \right)}}} \\{= {{{Pb\_ diff}{\_ y}{\_ dot}{\_ act}} + {{Vf\_ act}*}}} \\{{\sin \left( {{\delta f\_ act}*{\cos \left( {\theta \; {cf}} \right)}} \right)*\left( {{Lr}/L} \right)}}\end{matrix} & (53)\end{matrix}$

It should be noted that in the case where the magnitude of the value ofthe aforesaid conversion function Plfy(δf) corresponding to the actualsteering angle δf_act of the front wheel 3 f is sufficiently small (whenthe magnitude of δf_act is small), a differential value of the value ofPb_diff_y_act obtained by ignoring the second term on the right side ofthe expression (51) may be adopted as Pb_diff_y_dot_act for use in theexpression (53). That is, in the expression (53), a value, multiplied by−h′, of the differential value of the detected roll angle φb_act of thevehicle body 2 may be used instead of Pb_diff_y_dot_act. With thisconfiguration, the computational load of the control device 15 can bereduced.

Next, the control device 15 carries out the processing in the estimatedtraveling speed calculating section 33.

As shown in FIG. 18, the estimated traveling speed calculating section33 receives the aforesaid estimated front-wheel rotational transfervelocity Vf_act and the aforesaid detected front-wheel steering angleδf_act.

The estimated traveling speed calculating section 33 carries out theprocessing shown in the block diagram in FIG. 21 to calculate anestimated traveling speed Vox_act.

In FIG. 21, a processing section 33-1 represents a processing sectionwhich multiplies a detected front-wheel steering angle δf_act at thecurrent time by a cosine value of the caster angle θcf of the frontwheel 3 f (as in the aforesaid expression (52)) to obtain the estimatedfront-wheel effective steering angle δ′f_act, which has been describedabove in conjunction with the processing section 32-2 in the estimatedinverted pendulum mass point lateral velocity calculating section 32, aprocessing section 33-2 represents a processing section which obtains acosine value cos(δ′f_act) of the estimated front-wheel effectivesteering angle δ′f_act, and a processing section 33-3 represents aprocessing section which multiplies an estimated front-wheel rotationaltransfer velocity Vf_act at the current time by the above-describedcosine value cos(δ′f_act) to thereby calculate an estimated travelingspeed Vox_act.

Accordingly, the estimated traveling speed calculating section 33 isconfigured to calculate Vox_act by multiplying Vf_act by the cosinevalue cos(δ′f_act) of δ′f_act. That is, Vox_act is calculated by thefollowing expression (54).

$\begin{matrix}\begin{matrix}{{Vox\_ act} = {{Vf\_ act}*{\cos \left( {\delta^{\prime}{f\_ act}} \right)}}} \\{= {{Vf\_ act}*{\cos \left( {{\delta f\_ act}*{\cos \left( {\theta \; {cf}} \right)}} \right)}}}\end{matrix} & (54)\end{matrix}$

The estimated traveling speed Vox_act calculated in this mannercorresponds to a component in the X-axis direction of the estimatedfront-wheel rotational transfer velocity Vf_act.

It should be noted that for the estimated front-wheel effective steeringangle δ′f_act, the value calculated by the estimated inverted pendulummass point lateral velocity calculating section 32 as it is may be used.In this case, it is unnecessary to supply the detected front-wheelsteering angle δf_act to the estimated traveling speed calculatingsection 33, and the processing section 33-1 is also unnecessary.

Further, instead of the detected front-wheel steering angle δf_act andthe estimated front-wheel rotational transfer velocity Vf_act at thecurrent time, a value (last time's value) δf_cmd_p of the desiredfront-wheel steering angle δf_cmd, calculated by the posture controlarithmetic section 37 (described later) in the last time's controlprocessing cycle, and a value (last time's value) Vf_cmd_p of thedesired front-wheel rotational transfer velocity Vf_cmd, calculated bythe desired front-wheel rotational transfer velocity determining section36 (described later) in the last time's control processing cycle,respectively, may be used. More specifically, δf_cmd_p and Vf_cmd_p maybe used to perform computation similar to that in the right side of theabove expression (54), and the resultant value(=Vf_cmd_p*cos(δf_cmd_p*cos(θcf))) may be obtained as a pseudo estimate(alternative observed value) as an alternative to the estimatedtraveling speed Vox_act.

Further, in obtaining the pseudo estimate (alternative observed value)as an alternative to the estimated traveling speed Vox_act, δf_cmd_p maybe used instead of the detected front-wheel steering angle δf_act at thecurrent time, and the estimated front-wheel rotational transfer velocityVf_act may be used as it is. Conversely, Vf_cmd_p may be used instead ofthe estimated front-wheel rotational transfer velocity Vf_act at thecurrent time, and the detected front-wheel steering angle δf_act may beused as it is.

Furthermore, a value of the actual rotational transfer velocity of therear wheel 3 r estimated on the basis of an output from the rear-wheelrotational speed detector 21 (specifically, a value obtained bymultiplying the rotational angular velocity of the rear wheel 3 r,indicated by the output from the rear-wheel rotational speed detector21, by a predetermined effective rolling radius of the rear wheel 3 r)may be obtained as the estimated traveling speed Vox_act.

Next, the control device 15 carries out the processing in the desiredfront-wheel rotational transfer velocity determining section 36.

As shown in FIG. 18, the desired front-wheel rotational transfervelocity determining section 36 receives a detected value of the actualvalue of the accelerator manipulated variable, which is indicated by anoutput from the aforesaid accelerator manipulation detector 22.

The desired front-wheel rotational transfer velocity determining section36 determines a desired front-wheel rotational transfer velocity Vf_cmdby the processing shown in the block diagram in FIG. 25, i.e. theprocessing in a processing section 36-1.

The processing section 36-1 determines the desired front-wheelrotational transfer velocity Vf_cmd from a detected value of theaccelerator manipulated variable at the current time, by a presetconversion function.

The conversion function is a function which is defined, for example, bya mapping or an arithmetic expression. This conversion function isbasically set such that Vf_cmd determined by the conversion functionincreases monotonically as the accelerator manipulated variableincreases.

The conversion function is set, for example, with the trend asillustrated by the graph in FIG. 25. In this case, the processingsection 36-1 determines Vf_cmd to be zero when the detected value of theaccelerator manipulated variable falls within the dead band range (rangenear zero) from zero to a prescribed first accelerator manipulatedvariable A1.

Further, when the detected value of the accelerator manipulated variablefalls within the range from the first accelerator manipulated variableA1 to a prescribed second accelerator manipulated variable A2 (>A1), theprocessing section 36-1 determines Vf_cmd such that Vf_cmd increasesmonotonically as the accelerator manipulated variable increases and thatthe rate of increase of Vf_cmd (increase of Vf_cmd per unit increase ofthe accelerator manipulated variable) increases smoothly.

When the detected value of the accelerator manipulated variable fallswithin the range from the second accelerator manipulated variable A2 toa prescribed third accelerator manipulated variable A3 (>A2), theprocessing section 36-1 determines Vf_cmd such that Vf_cmd increasesmonotonically, at a constant rate of increase, as the acceleratormanipulated variable increases.

Further, when the detected value of the accelerator manipulated variableexceeds the third accelerator manipulated variable A3, the processingsection 36-1 determines Vf_cmd such that it remains at a constant value(at the value corresponding to A3).

Next, the control device 15 carries out the processing in the controlgain determining section 35. As shown in FIG. 18, the control gaindetermining section 35 receives, via a delay element 39, a last time'sdesired front-wheel steering angle δf_cmd_p, which is a value (lasttime's value) of the desired front-wheel steering angle δf_cmddetermined by the posture control arithmetic section 37 in the lasttime's control processing cycle of the control device 15. The controlgain determining section 35 also receives an estimated traveling speedVox_act calculated by the estimated traveling speed calculating section33 in the current time's control processing cycle.

The control gain determining section 35 carries out the processing shownin the block diagram in FIG. 22, for example, to determine values of aplurality of gains K1, K2, K3, K4, and Kh for the posture control of thevehicle body 2.

The values of the gains K1, K2, K3, K4, and Kh are each determinedvariably in accordance with δf_cmd_p and Vox_act, or in accordance withVox_act, as will be described in detail later.

Next, the control device 15 carries out the processing in the desiredposture state determining section 34. The desired posture statedetermining section 34 determines a desired inverted pendulum mass pointlateral movement amount Pb_diff_y_cmd, which is a desired value of theinverted pendulum mass point lateral movement amount Pb_diff_y, and adesired inverted pendulum mass point lateral velocity Vby_cmd, which isa desired value of the inverted pendulum mass point lateral velocityVby. In the present embodiment, the desired posture state determiningsection 34 sets both of Pb_diff_y_cmd and Vby_cmd to zero, by way ofexample.

Next, the control device 15 carries out the processing in the posturecontrol arithmetic section 37. As shown in FIG. 18, the posture controlarithmetic section 37 receives the desired inverted pendulum mass pointlateral movement amount Pb_diff_y_cmd and the desired inverted pendulummass point lateral velocity Vby_cmd determined in the desired posturestate determining section 34, the estimated inverted pendulum mass pointlateral movement amount Pb_diff_y_act calculated in the estimatedinverted pendulum mass point lateral movement amount calculating section31, the estimated inverted pendulum mass point lateral velocity Vby_actcalculated in the estimated inverted pendulum mass point lateralvelocity calculating section 32, the gains K1, K2, K3, K4, and Khdetermined in the control gain determining section 35, and a detectedvalue Th_act (hereinafter, referred to as “detected handlebar torqueTh_act”) of the actual value of the handlebar torque Th, indicated by anoutput from the aforesaid handlebar torque detector 19.

The posture control arithmetic section 37 uses the above-described inputvalues to carry out the processing shown in the block diagram in FIG.26, to thereby determine a desired front-wheel steering angle δf_cmd, adesired front-wheel steering angular velocity δf_dot_cmd, and a desiredfront-wheel steering angular acceleration δf_dot2_cmd.

In FIG. 26, a processing section 37-1 represents a processing sectionwhich multiplies Th_act by the gain Kh to convert Th_act into a requiredvalue of the angular acceleration of the steering angle of the frontwheel 3 f, a processing section 37-2 represents a processing sectionwhich obtains a deviation of Pb_diff_y_act from Pb_diff_y_cmd, aprocessing section 37-3 represents a processing section which multipliesthe output of the processing section 37-2 by the gain K1, a processingsection 37-4 represents a processing section which obtains a deviationof Vby_act from Vby_cmd, a processing section 37-5 represents aprocessing section which multiplies the output of the processing section37-4 by the gain K2, a processing section 37-6 represents a processingsection which multiplies δf_cmd_p by the gain K3, a processing section37-7 represents a processing section which multiplies a last time'sdesired front-wheel steering angular velocity δf_dot_cmd_p, which is avalue of the desired front-wheel steering angular velocity δf_dot_cmddetermined by the posture control arithmetic section 37 in the lasttime's control processing cycle, by the gain K4, a processing section37-8 represents a processing section which calculates a sum of theoutputs from the processing sections 37-3 and 37-5 and the values, eachmultiplied by −1, of the outputs from the processing sections 37-6 and37-7, and a processing section 37-9 represents a processing sectionwhich sums up the outputs from the processing sections 37-8 and 37-1 tothereby calculate a desired front-wheel steering angular accelerationδf_dot2_cmd.

Further, a processing section 37-10 represents a processing sectionwhich integrates the output of the processing section 37-9 to obtain adesired front-wheel steering angular velocity δf_dot_cmd, a processingsection 37-11 represents a delay element which outputs the output fromthe processing section 37-10 in the last time's control processing cycle(i.e. last time's desired front-wheel steering angular velocityδf_dot_cmd_p) to the processing section 37-7, a processing section 37-12represents a processing section which integrates the output of theprocessing section 37-10 to obtain a desired front-wheel steering angleδf_cmd, and a processing section 37-13 represents a delay element whichoutputs the output from the processing section 37-12 in the last time'scontrol processing cycle (i.e. last time's desired front-wheel steeringangle δf_cmd_p) to the processing section 37-6.

Accordingly, the posture control arithmetic section 37 calculates thedesired front-wheel steering angular acceleration δf_dot2_cmd by thefollowing expression (55).

$\begin{matrix}{{{{\delta f\_ dot2}{\_ cmd}} = {\left( {{K\; 1*\left( {{{Pb\_ diff}{\_ y}{\_ cmd}} - {{Pb\_ diff}{\_ y}{\_ act}}} \right)} + {K\; 2*\left( {{Vby\_ cmd} - {Vby\_ act}} \right)} - {K\; 3*{\delta f\_ cmd}{\_ p}} - {K\; 4*{\delta f\_ dot}{\_ cmd}{\_ p}}} \right) + {{Kh}*{Th\_ act}}}}\;} & (55)\end{matrix}$

In the above expression (55), K1*(Pb_diff_y_cmd−Pb_diff_y_act) is afeedback manipulated variable having the function of making thedeviation (Pb_diff_y_cmd−Pb_diff_y_act) approach “0”,K2*(Vby_cmd−Vby_act) is a feedback manipulated variable having thefunction of making the deviation (Vby_cmd−Vby_act) approach “0”,−K3*δf_cmd_p is a feedback manipulated variable having the function ofmaking δf_cmd approach “0”, and −K4*δf_dot_cmd_p is a feedbackmanipulated variable having the function of making δf_dot_cmd approach“0”.

Further, Kh*Th_act is a feedforward manipulated variable correspondingto the actual handlebar torque (detected handlebar torque Th_act)applied to the steering handlebar 7 by the rider.

The posture control arithmetic section 37 integrates δf_dot2_cmddetermined by the above expression (55) to determine a desiredfront-wheel steering angular velocity δf_dot_cmd. Further, the posturecontrol arithmetic section 37 integrates this δf_dot_cmd to determine adesired front-wheel steering angle δf_cmd.

It should be noted that δf_cmd_p and δf_dot_cmd_p used in thecomputation of the expression (55) have the meanings as pseudo estimates(alternative observed values) of the actual steering angle and steeringangular velocity, respectively, of the front wheel 3 f at the currenttime. Therefore, instead of δf_cmd_p, a detected front-wheel steeringangle δf_act at the current time may be used. Further, instead ofδf_dot_cmd_p, a detected front-wheel steering angular velocityδf_dot_act (detected value of the actual steering angular velocity ofthe front wheel 3 f) based on an output from the aforesaid front-wheelsteering angle detector 17 may be used.

The above has described the processing in the posture control arithmeticsection 37.

In accordance with the processing in the posture control arithmeticsection 37, the desired front-wheel steering angular accelerationδf_dot2_cmd is basically determined, in the case where no handlebartorque Th is applied to the steering handlebar 7, such that anydivergence of the actual inverted pendulum mass point lateral movementamount (estimated inverted pendulum mass point lateral movement amountPb_diff_y_act) of the two-wheeled vehicle 1A from the desired invertedpendulum mass point lateral movement amount Pb_diff_y_cmd, or anydivergence of the actual inverted pendulum mass point lateral velocity(estimated inverted pendulum mass point lateral velocity Vby_act) of thetwo-wheeled vehicle 1A from the desired inverted pendulum mass pointlateral velocity Vby_cmd, is eliminated through manipulation of thesteering angle δf of the front wheel 3 f (and, hence, that the actualinverted pendulum mass point lateral movement amount or lateral velocityof the two-wheeled vehicle 1A is restored to the desired invertedpendulum mass point lateral movement amount Pb_diff_y_cmd or desiredinverted pendulum mass point lateral velocity Vby_cmd).

Further, in the present embodiment, the desired inverted pendulum masspoint lateral movement amount Pb_diff_y_cmd is “0”. Therefore, in thestate where the actual inverted pendulum mass point lateral movementamount of the two-wheeled vehicle 1A is held at a value which coincides,or almost coincides, with the desired inverted pendulum mass pointlateral movement amount Pb_diff_y_cmd, the desired front-wheel steeringangular acceleration δf_dot2_cmd is determined so as to keep the actualsteering angle of the front wheel 3 f at “0” or almost “0”.

Furthermore, in the case where a handlebar torque Th is applied to thesteering handlebar 7, a feedforward manipulated variable correspondingto the detected handlebar torque Th_act is added to the desiredfront-wheel steering angular acceleration δf_dot2_cmd.

It should be noted that, instead of adding the feedforward manipulatedvariable corresponding to the detected handlebar torque Th_act toδf_dot2_cmd as described above, it may be configured to add thefeedforward manipulated variable corresponding to the detected handlebartorque Th_act (value obtained by multiplying Th_act by a gain) to thedesired front-wheel steering angular velocity δf_dot_cmd or to thedesired front-wheel steering angle δf_cmd.

Alternatively, instead of adding the feedforward manipulated variablecorresponding to the detected handlebar torque Th_act to δf_dot2_cmd, itmay be configured to correct the desired inverted pendulum mass pointlateral movement amount Pb_diff_y_cmd in accordance with Th_act and touse the corrected desired inverted pendulum mass point lateral movementamount instead of Pb_diff_y_cmd, as shown, for example, in the blockdiagram in FIG. 27.

In the processing in the posture control arithmetic section 37 shown inthe block diagram in FIG. 27, a processing section 37-14 is providedinstead of the processing section 37-9 shown in FIG. 26. The processingsection 37-14 subtracts the output of the processing section 37-1(=Kh*Th_act) from the desired inverted pendulum mass point lateralmovement amount Pb_diff_y_cmd to correct Pb_diff_y_cmd. It should benoted that the value of the gain Kh by which Th_act is multiplied inthis case is usually different from the value of the gain Kh used in theprocessing section 37-1 in the block diagram in FIG. 26.

The processing section 37-14 then supplies the corrected desiredinverted pendulum mass point lateral movement amount(=Pb_diff_y_cmd−Kh*Th_act) to the processing section 37-2, instead ofPb_diff_y_cmd.

Further, in the processing in the block diagram in FIG. 27, the outputfrom the processing section 37-8, as it is, is determined to be adesired front-wheel steering angular acceleration δf_dot2_cmd, and issupplied to the processing section 37-10.

In other respects, the processing shown in the block diagram in FIG. 27is identical to that shown in FIG. 26.

Accordingly, in the processing in the posture control arithmetic section37 shown in FIG. 27, the desired front-wheel steering angularacceleration δf_dot2_cmd is calculated by the following expression (56).

$\begin{matrix}{{{\delta f\_ dot2}{\_ cmd}} = {{K\; 1*\left( {\left( {{{Pb\_ diff}{\_ y}{\_ cmd}} - {{Kh}*{Th\_ act}}} \right) - {{Pb\_ diff}{\_ y}{\_ act}}} \right)} + {K\; 2*\left( {{Vby\_ cmd} - {Vby\_ act}} \right)} - {K\; 3*{\delta f\_ cmd}{\_ p}} - {K\; 4*{\delta f\_ dot}{\_ cmd}{\_ p}}}} & (56)\end{matrix}$

When the value of the gain Kh used in the processing section 37-1 in theblock diagram in FIG. 26 is divided by the gain K1 and the obtainedvalue is multiplied by −1, and when the resultant value is used as thegain Kh in the processing section 37-1 in the block diagram in FIG. 27,then the block diagram in FIG. 27 becomes equivalent to the blockdiagram in FIG. 26.

In the block diagram in FIG. 26 or the block diagram in FIG. 27, a valueobtained by multiplying the detected handlebar torque Th_act by aprescribed gain may be added to the output of the processing section37-10.

Alternatively, in the block diagram in FIG. 26 or the block diagram inFIG. 27, a value obtained by multiplying the detected handlebar torqueTh_act by a prescribed gain may be added to the output of the processingsection 37-12.

Still alternatively, instead of the detected handlebar torque Th_act asit is, the detected handlebar torque Th_act which has been passedthrough a filter for adjusting frequency characteristics may be used.Adding the processes as described above can make the control system'sresponse characteristics to the handlebar torque further suit the tasteof the rider of the two-wheeled vehicle 1A.

Here, the gains K1 to K4 (feedback gains related to the respectivefeedback manipulated variables in the right side of the aforesaidexpression (55)) and the gain Kh, which are used for calculatingδf_dot2_cmd by the computation of the expression (55), are determined inthe aforesaid control gain determining section 35. The processing in thecontrol gain determining section 35 will now be described in detail.

The control gain determining section 35 determines the values of thegains K1 to K4 and Kh from the received estimated traveling speedVox_act and last time's desired front-wheel steering angle δf_cmd_p, bythe processing shown in the block diagram in FIG. 22.

In FIG. 22, a processing section 35-1 is a processing section whichdetermines the gain K1 in accordance with Vox_act and δf_cmd_p, and aprocessing section 35-2 is a processing section which determines thegain K2 in accordance with Vox_act and δf_cmd_p.

In the present embodiment, the processing section 35-1 determines thegain K1 from Vox_act and δf_cmd_p, in accordance with a presettwo-dimensional mapping (conversion function of two variables).Similarly, the processing section 35-2 determines the gain K2 fromVox_act and δf_cmd_p, in accordance with a preset two-dimensionalmapping (conversion function of two variables).

In these two-dimensional mappings, the trend of the change in value ofthe gain K1 with respect to Vox_act and δf_cmd_p and the trend of thechange in value of the gain K2 with respect to Vox_act and δf_cmd_p areset substantially similar to each other.

Specifically, as illustrated by the graphs shown in the processingsections 35-1 and 35-2 in FIG. 22, the two-dimensional mappings in theprocessing sections 35-1 and 35-2 are each set such that the magnitudeof the gain K1, K2 determined by the two-dimensional mapping has thetrend of monotonically decreasing with increasing Vox_act when δf_cmd_pis fixed to a given value.

Accordingly, the gains K1 and K2 as the feedback gains related to thefeedback manipulated variables having the function of stabilizing theposture in the roll direction of the vehicle body 2 of the two-wheeledvehicle 1A (making the estimated inverted pendulum mass point lateralmovement amount Pb_diff_y_act and the estimated inverted pendulum masspoint lateral velocity Vby act converge respectively to Pb_diff_y_cmdand Vby_cmd) are determined such that the magnitudes of the gains K1 andK2 each become smaller as the actual traveling speed (estimatedtraveling speed Vox_act) of the two-wheeled vehicle 1A becomes greater.

In other words, the gains K1 and K2 are determined such that the controlfunction for stabilizing the posture in the roll direction of thevehicle body 2 by performing the steering control of the front wheel 3 fso as to make Pb_diff_y_act and Vby_act converge to Pb_diff_y_cmd andVby_cmd, respectively, is reduced when the actual traveling speed(estimated traveling speed Vox_act) of the two-wheeled vehicle 1A is ina high-speed range, as compared to when it is in a low-speed range.

Accordingly, in the case where the actual traveling speed (estimatedtraveling speed Vox_act) of the two-wheeled vehicle 1A is relativelyhigh, i.e. in the state where the posture in the roll direction of thevehicle body 2 is unlikely to become unstable, a rider of thetwo-wheeled vehicle 1A can readily change the posture in the rolldirection (roll angle φb) of the vehicle body 2 by shifting the weightof the rider's body and so on, as in the case of a conventionaltwo-wheeled vehicle (which is not provided with the function ofcontrolling the posture in the roll direction of the vehicle body).

It should be noted that the two-dimensional mappings for determining thegains K1 and K2 may each be set such that the value of K1, K2 isdetermined to be “0” or almost “0” when the estimated traveling speedVox_act reaches a certain level of speed.

With this configuration, the function of controlling the posture in theroll direction of the vehicle body 2 becomes substantially OFF when theactual traveling speed (estimated traveling speed Vox_act) of thetwo-wheeled vehicle 1A is relatively high. This can make the behavioralcharacteristics of the two-wheeled vehicle 1A approach thecharacteristics comparable to those of a conventional two-wheeledvehicle in the case where the actual traveling speed of the two-wheeledvehicle 1A is high.

Further, the two-dimensional mappings in the processing sections 35-1and 35-2 are each set such that the gain K1, K2 determined by themapping has the trend of monotonically decreasing with increasingmagnitude (absolute value) of δf_cmd_p when Vox_act is fixed to a givenvalue.

Accordingly, the gains K1 and K2 as the gains related to the feedbackmanipulated variables having the function of stabilizing the posture inthe roll direction of the vehicle body 2 of the two-wheeled vehicle 1Aare determined such that the magnitudes of the gains K1 and K2 eachbecome smaller as the magnitude of δf_cmd_p, corresponding to the actualsteering angle of the front wheel 3 f, becomes larger.

The magnitudes of the gains K1 and K2 are changed as described above,for the following reason. In the case where the magnitude of the actualsteering angle of the front wheel 3 f is large, compared to the casewhere it is small, the radius of curvature of the ground contact part ofthe steering control wheel (front wheel 30 as seen in a cross sectionincluding the ground contact point of the steering control wheel (frontwheel 3 f) and having a normal in the X-axis direction (longitudinaldirection of the vehicle body 2) becomes larger, as explained above.

Therefore, in the case where the magnitude of the actual steering angleof the front wheel 3 f is large, compared to the case where it is small,the change in movement amount of the ground contact point of the frontwheel 3 f according to the change in the steering becomes larger.Because of this, if the magnitudes of the gains K1 and K2 are setindependently of the actual steering angle, oscillation is likely tooccur in the control of the posture in the roll direction of the vehiclebody 2 of the two-wheeled vehicle 1A.

When it is configured such that the magnitudes of the gains K1 and K2are changed in accordance with the magnitude of δf_cmd_p, as describedabove, the above-described oscillation can be prevented even in the casewhere the magnitude (absolute value) of the actual steering angle of thefront wheel 3 f is large.

In the block diagram in FIG. 22, processing sections 35-3 and 35-4represent processing sections which determine the gains K3 and K4,respectively, in accordance with Vox_act.

In the present embodiment, the processing sections 35-3 and 35-4determine the gains K3 and K4, respectively, from Vox_act, in accordancewith conversion functions defined by preset mappings (or arithmeticexpressions).

These conversion functions are set, as illustrated by the graphs shownin the processing sections 35-3 and 35-4 in FIG. 22, such that basicallythe gains K3 and K4 each increase monotonically, between a prescribedupper limit and a prescribed lower limit, as Vox_act increases.

In this case, in the conversion functions in the processing sections35-3 and 35-4, in the region where Vox_act takes a value near “0”, K3and K4 are each maintained at the lower limit. In the region whereVox_act takes a sufficiently large value, K3 and K4 are each maintainedat the upper limit.

As the gains K3 and K4 are determined in the above-described manner, thegains K3 and K4 as the feedback gains related to the feedbackmanipulated variables having the function of making the steering angleof the front wheel 3 f approach zero are determined such that themagnitudes of the gains K3 and K4 become relatively large in the casewhere the actual traveling speed (estimated traveling speed Vox_act) ofthe two-wheeled vehicle 1A is relatively high (in a high-speed range),compared to the case where the actual traveling speed of the two-wheeledvehicle 1A is relatively low (in a low-speed range (including “0”)).

Here, in an ordinary two-wheeled vehicle, when it is traveling at arelatively high speed, the steering control wheel is usually held in anon-steered state or nearly non-steered state. Therefore, setting thegains K3 and K4 in the above-described manner can allow the steeringcharacteristics of the front wheel 3 f of the two-wheeled vehicle 1Awhen the actual traveling speed of the two-wheeled vehicle 1A isrelatively high to approach the characteristics of the ordinarytwo-wheeled vehicle.

Further, in FIG. 22, a processing section 35-5 represents a processingsection which determines the gain Kh in accordance with Vox_act.

In the present embodiment, the processing section 35-5 determines thegain Kh from Vox_act, in accordance with a conversion function definedby a preset mapping (or arithmetic expression), as with the gains K3 andK4.

This conversion function is set, as illustrated by the graph shown inthe processing section 35-5 in FIG. 22, such that basically themagnitude of the gain Kh becomes relatively large when Vox_act is largeas compared to when Vox_act is small.

In this case, the conversion function in the processing section 35-5 isset such that the gain Kh increases monotonically, between a prescribedupper limit and a prescribed lower limit, as Vox_act increases. Further,the conversion function is set such that the Kh determined thereby hassaturation characteristics with respect to Vox_act. That is, Kh isdetermined by the conversion function such that the magnitude of therate of change of the value of Kh with respect to Vox_act (increase ofKh per unit increase of Vox_act) becomes smaller in a low-speed range inwhich Vox_act takes a value near “0” (including “0”) and a high-speedrange in which Vox_act takes a sufficiently large value, than in amid-speed range between the low-speed range and the high-speed range.

Determining the gain Kh in accordance with Vox_act in this mannerensures that the magnitude of the gain Kh relative to the gain K1becomes large when the actual traveling speed of the two-wheeled vehicle1A is relatively high.

Accordingly, when a rider applies a torque about the handlebar axis Chto the steering handlebar 7 in an attempt to move the steering handlebar7, the desired front-wheel steering angular acceleration δf_dot2_cmd isdetermined so as to bring the detected handlebar torque Th_act to zero.This leads to improved tracking of the steering of the front wheel 3 fto the rider's moving the steering handlebar 7.

As a result, during high-speed traveling of the two-wheeled vehicle 1A,the rider can steer the front wheel 3 f by manipulating the steeringhandlebar 7, similarly as in a conventional two-wheeled vehicle.

The above has described the details of the processing in the controlgain determining section 35 according to the present embodiment.

In the processing in the aforesaid processing sections 35-1 and 35-2,the gains K1 and K2 were determined in accordance with Vox_act andδf_cmd_p by using two-dimensional mappings. The gains K1 and K2,however, may be determined in another manner without using thetwo-dimensional mappings.

For example, the gains K1 and K2 may be determined by the processing inprocessing sections 35-6 and 35-7 in the block diagram in FIG. 23 or 24.It should be noted that, except for the processing in the processingsections 35-6 and 35-7, the processing in the block diagram in each ofFIGS. 23 and 24 is identical to the processing in the block diagram inFIG. 22.

The processing section 35-6 in FIG. 23 includes a processing section35-6-1 which determines a first adjustment parameter Kv_(—)1 foradjusting the value of the gain K1, from Vox_act, by a preset conversionfunction, a processing section 35-6-2 which determines a secondadjustment parameter Kδ_(—)1 for adjusting the value of the gain K1,from δf_cmd_p, by a preset conversion function, a processing section35-6-3 which determines a composite adjustment parameter(=Kv_(—)1*Kδ_(—)1) by multiplying the adjustment parameters Kv_(—)1 andKδ_(—)1, and a processing section 35-6-4 which adds this compositeadjustment parameter to a prescribed reference value (lower limit)K0_(—)1 of the gain K1, to thereby determine the gain K1(=Kv_(—)1*Kδ_(—)1+K0_(—)1).

The processing section 35-7 includes a processing section 35-7-1 whichdetermines a first adjustment parameter Kv_(—)2 for adjusting the valueof the gain K2, from Vox_act, by a preset conversion function, aprocessing section 35-7-2 which determines a second adjustment parameterKδ_(—)2 for adjusting the value of the gain K2, from δf_cmd_p, by apreset conversion function, a processing section 35-7-3 which determinesa composite adjustment parameter (=Kv_(—)2*Kδ_(—)2) by multiplying theadjustment parameters Kv_(—)2 and Kδ_(—)2, and a processing section35-7-4 which adds this composite adjustment parameter to a prescribedreference value (lower limit) K0_(—)2 of the gain K2, to therebydetermine the gain K2 (=Kv_(—)2*Kδ_(—)2+K0_(—)2).

In this case, the conversion functions of the respective processingsections 35-6-1, 35-7-1, 35-6-2, and 35-7-2 are each defined, forexample, by a mapping (one-dimensional mapping) or an arithmeticexpression.

The conversion functions of the processing sections 35-6-1 and 35-7-1are set, as illustrated by the graphs shown in the processing sections35-6-1 and 35-7-1 in FIG. 23, such that Kv_(—)1 and Kv_(—)2 determinedby the respective conversion functions each decrease monotonically (toapproach zero) from a prescribed upper limit (>0) as Vox_act becomeslarger.

Accordingly, in a low-speed range where Vox_act is relative low, Kv_(—)1and Kv_(—)2 are each set to an effective positive value (having amagnitude above a certain level).

Further, the conversion functions of the processing sections 35-6-2 and35-7-2 are set, as illustrated by the graphs shown in the processingsections 35-6-2 and 35-7-2 in FIG. 23, such that Kδ_(—)1 and Kδ_(—)2determined by the respective conversion functions each decreasemonotonically as the magnitude (absolute value) of δf_cmd_p increases.

More specifically, Kδ_(—)1 and Kδ_(—)2 are determined such that theyeach take a prescribed upper limit (>0) when the magnitude of δf_cmd_pis “0”, and that Kδ_(—)1 and Kδ_(—)2 each decrease down to a prescribedlower limit (>0) as the magnitude of δf_cmd_p increases from “0”.

Therefore, the processing sections 35-6 and 35-7 shown in FIG. 23 candetermine the gains K1 and K2, respectively, such that the trends of thechanges of K1 and K2 with respect to Vox_act and δf_cmd_p become similarto the trends of the changes of K1 and K2 determined by the processingsections 35-1 and 35-2, respectively, in FIG. 22.

The processing sections 35-6 and 35-7 in FIG. 24 are different fromthose in FIG. 23 only in part of the processing.

Specifically, the processing section 35-6 in FIG. 24 adopts a processingsection 35-6-5 as a processing section for determining the firstadjustment parameter Kv_(—)1 for adjusting the value of the gain K1 inaccordance with Vox_act, instead of the processing section 35-6-1 shownin FIG. 23. Except for the processing section 35-6-5, the configurationof the processing section 35-6 in FIG. 24 is identical to that in FIG.23.

Similarly, the processing section 35-7 in FIG. 24 adopts a processingsection 35-7-5, instead of the processing section 35-7-1 shown in FIG.23, as a processing section for determining the first adjustmentparameter Kv_(—)2 for adjusting the value of the gain K2 in accordancewith Vox_act. Except for the processing section 35-7-5, theconfiguration of the processing section 35-7 in FIG. 24 is identical tothat in FIG. 23.

The processing sections 35-6-5 and 35-7-5 use, for determining Kv_(—)1and Kv_(—)2, respectively, conversion functions (mappings or arithmeticexpressions) which are different from those used in FIG. 23.

Specifically, the conversion functions in the processing sections 35-6-5and 35-7-5 are set, as illustrated by the graphs shown in the processingsections 35-6-5 and 35-7-5 in FIG. 24, such that Kv_(—)1 and Kv_(—)2determined by the respective conversion functions each monotonicallydecrease with increasing Vox_act and, additionally, such that Kv_(—)1and Kv_(—)2 are each set to zero (or almost zero) in a high-speed rangewhere Vox_act becomes high.

It should be noted that the reference value (lower limit) K0_(—)1 of thegain K1 in the processing section 35-6 in FIG. 24 and the referencevalue (lower limit) K0_(—)2 of the gain K2 in the processing section35-7 in FIG. 24 are each set to zero or a value near zero.

Therefore, the processing sections 35-6 and 35-7 shown in FIG. 24 candetermine the gains K1 and K2, respectively, such that the trends of thechanges of K1 and K2 with respect to Vox_act and δf_cmd_p become similarto the trends of the changes of K1 and K2 determined by the processingsections 35-1 and 35-2, respectively, in FIG. 22.

In addition, in a high-speed range where the actual traveling speed ofthe two-wheeled vehicle 1A is high, both of the gains K1 and K2 are setto zero or almost zero. This can make the behavioral characteristics ofthe two-wheeled vehicle 1A still further approach the characteristicscomparable to those of a conventional two-wheeled vehicle in the casewhere the actual traveling speed of the two-wheeled vehicle 1A is high.

It should be noted that for the conversion functions for determining thegains K1 and K2, conversion functions in other forms may be adopted, aslong as they can determine the gains with the above-described trendswith respect to Vox_act and δf_cmd_p. Similarly, for the conversionfunctions for determining the gains K3, K4, and Kh, conversion functionsin other forms may be adopted, as long as they can determine the gainswith the above-described trends with respect to Vox_act.

Supplementally, the last time's desired front-wheel steering angleδf_cmd_p has the meaning as a pseudo estimate (alternative observedvalue) of the actual steering angle of the front wheel 3 f at thecurrent time.

Accordingly, for determining the respective gains K1, K2, K3, K4, andKh, the aforesaid detected front-wheel steering angle δf_act may be usedinstead of δf_cmd_p.

Further, in the case where the response of the front-wheel drivingactuator 10 is sufficiently quick, the value of the traveling speed(=Vf_cmd_p*cos(δf_cmd_p*cos(θcf)), hereinafter referred to as “lasttime's desired traveling speed Vox_cmd_p”) calculated by the computationsimilar to that in the aforesaid expression (54) from theabove-described last time's desired front-wheel steering angle δf_cmd_pand a last time's desired front-wheel rotational transfer velocityVf_cmd_p (desired front-wheel rotational transfer velocity Vf_cmddetermined by the desired front-wheel rotational transfer velocitydetermining section 36 in the last time's control processing cycle) hasthe meaning as a pseudo estimate (alternative observed value) of theactual traveling speed of the two-wheeled vehicle 1A at the currenttime.

Accordingly, for determining the respective gains K1, K2, K3, K4, andKh, the above-described last time's desired traveling speed Vox_cmd_pmay be used instead of Vox_act.

After the control device 15 has determined the desired front-wheelsteering angle δf_cmd in the posture control arithmetic section 37 asdescribed above, the control device 15 carries out the processing in thedesired handlebar angle determining section 38.

The desired handlebar angle determining section 38 receives, as shown inFIG. 18, the estimated traveling speed Vox_act calculated in theestimated traveling speed calculating section 33 and the desiredfront-wheel steering angle δf_cmd determined in the posture controlarithmetic section 37.

The desired handlebar angle determining section 38 uses these inputvalues to carry out the processing shown in the block diagram in FIG.28, to thereby determine a desired handlebar angle δh_cmd and a desiredhandlebar angular velocity δh_dot_cmd.

In FIG. 28, a processing section 38-1 is a processing section whichdetermines a correction factor Kh_v for correcting δf_cmd, in accordancewith the estimated traveling speed Vox_act, a processing section 38-2 isa processing section which corrects δf_cmd by multiplying δf_cmd by theoutput (correction factor Kh_v) from the processing section 38-1, aprocessing section 38-3 is a processing section which determines adesired handlebar angle δh_cmd from the output (=Kh_v*δf_cmd) from theprocessing section 38-2, and a processing section 38-4 is a processingsection which calculates a temporal change rate (amount of change perunit time) of the output (δh_cmd) from the processing section 38-3, as adesired handlebar angular velocity δh_dot_cmd.

Accordingly, the desired handlebar angle determining section 38determines a desired handlebar angle δh_cmd in accordance with thecorrected value (=Kh_v*δf_cmd, this corrected value will be hereinafterreferred to as “corrected desired front-wheel steering angle δf_cmd_c”)obtained by correcting δf_cmd in accordance with Vox_act. Further, thedesired handlebar angle determining section 38 differentiates thisδh_cmd to determine a desired handlebar angular velocity δh_dot_cmd.

In this case, the correction factor Kh_v takes a positive value of 1 orless. The correction factor Kh_v is determined from the estimatedtraveling speed Vox_act, by a preset conversion function. The conversionfunction is defined, for example, by a mapping or an arithmeticexpression. The conversion function is set to show the trend asillustrated by the graph shown in the processing section 38-1 in FIG.28.

Here, when the two-wheeled vehicle 1A is stationary or traveling at avery low speed, the posture restoring force in the roll direction of thevehicle body 2 per unit steering angle of the front wheel 3 f is weakand, therefore, the front wheel 3 f needs to be steered relativelylargely for stabilizing the posture.

In such a case, if it is set such that the steering angle of the frontwheel 3 f coincides with the handlebar angle Oh as in a conventionaltwo-wheeled vehicle in which the steering handlebar is directlyconnected to the steering shaft of the front wheel, the large steeringof the front wheel 3 f will cause the steering handlebar 7 to rotatelargely, giving a sense of discomfort to the rider of the two-wheeledvehicle 1A. The steering handlebar 7 may also interfere with a part ofthe vehicle body 2 close to the steering handlebar 7.

In order to solve the above problems, in the present embodiment, theconversion function in the processing section 38-1 has been set, asillustrated by the graph in the figure, such that the correction factorKh_v becomes smaller as Vox_act becomes smaller (as the actual travelingspeed of the two-wheeled vehicle 1A becomes lower).

This correction factor Kh_v basically has the function of changing theratio of the amount of change of the handlebar angle δ to the unitamount of change of the steering angle δf of the front wheel 3 f, i.e. aso-called steering gear ratio, in accordance with Vox_act. Therefore, itis set such that the above-described ratio becomes smaller as Vox_actbecomes smaller.

More specifically, the conversion function in the processing section38-1 is set such that the above-described ratio (correction factor Kh_v)becomes “1” or almost “1” when Vox_act becomes a prescribed speed orhigher and that the ratio becomes less than “1” when Vox_act becomeslower than the prescribed speed.

As a result, when the two-wheeled vehicle 1A is stationary or travelingat a very low speed, even if the steering angle of the front wheel 3 fbecomes large for the purpose of stabilizing the posture of the vehiclebody 2, the handlebar angle δh is restricted to a small angle. This canreduce the sense of discomfort of the rider of the two-wheeled vehicle1A and also prevent the interference between the steering handlebar 7and the vehicle body 2.

Furthermore, in the present embodiment, when the processing section 38-3determines a desired handlebar angle δh_cmd from the corrected desiredfront-wheel steering angle δf_cmd_c which is δf_cmd corrected with thecorrection factor Kh_v, it determines δh_cmd in accordance with aconversion function which has been preset to cause δh_cmd to havesaturation characteristics with respect to δf_cmd_c. The saturationcharacteristics means the characteristics that the magnitude of the rateof change of δh_cmd with respect to δf_cmd_c (amount of change of δh_cmdper unit amount of change of δf_cmd_c) becomes smaller when themagnitude of δh_cmd_c is large, as compared to when the magnitude ofδh_cmd_c is small.

The conversion function in the processing section 38-3 having suchsaturation characteristics is defined, for example, by a mapping or anarithmetic expression. The conversion function is set, for example, asillustrated by the graph shown in the processing section 38-3 in FIG.28.

In this example, δh_cmd is determined such that, when the magnitude(absolute value) of δf_cmd_c is not greater than a prescribed value,δh_cmd changes monotonically up to an upper limit on the positive sideor down to a lower limit on the negative side in response to the changeof δf_cmd_c (or δf_cmd) to the positive side or the negative side,respectively. In this situation, δh_cmd is determined, for example, tocoincide with, or almost coincide with, δf_cmd_c.

When the magnitude (absolute value) of δf_cmd_c exceeds the prescribedvalue, δh_cmd is maintained constantly at the upper limit on thepositive side or the lower limit on the negative side.

Determining δh_cmd so as to have saturation characteristics with respectto δf_cmd_c in the above-described manner can prevent the actualhandlebar angle (detected handlebar angle δh_act) from becomingexcessively large.

It should be noted that the processing of determining δh_cmd fromδf_cmd_c may be carried out by using, for example, a conversion function(having saturation characteristics) as illustrated by the graph shown ina processing section 38-5 in the block diagram in FIG. 29. Thisconversion function, defined by a mapping or an arithmetic expression,is set such that the magnitude of the rate of change of δh_cmd withrespect to δf_cmd_c becomes continuously smaller as the magnitude ofδf_cmd_c becomes larger. The minimum value of the magnitude of theabove-described rate of change may be greater than zero.

When the conversion function in the processing section 38-5 is set inthe above-described manner, the rate of change of δh_cmd with respect toδf_cmd (amount of change of δh_cmd per unit increase of δf_cmd) can bemade to change continuously. Consequently, the angular acceleration ofthe actual handlebar angle can be made to change continuously. This canrestrict an abrupt change in rotational angular velocity (angularvelocity about the handlebar axis Ch) of the steering handlebar 7. As aresult, the sense of discomfort of the rider during the manipulation ofthe steering handlebar 7 can further be reduced. The load of thehandlebar driving actuator 9 can be reduced as well.

It should be noted that δh_cmd may be determined from δf_cmd and Vox_actby a two-dimensional mapping. Further, as Vox_act for determiningδh_cmd, the value of the actual rotational transfer velocity of the rearwheel 3 r, estimated on the basis of an output from the rear-wheelrotational speed detector 21, may be used. Alternatively, the aforesaidlast time's desired traveling speed Vox_cmd_p, calculated by thecomputation similar to that in the right side of the aforesaidexpression (54) from the last time's desired front-wheel steering angleδf_cmd_p and the last time's desired front-wheel rotational transfervelocity Vf_cmd_p, may be used instead of Vox_act.

Controls of the aforesaid front-wheel steering actuator 8, handlebardriving actuator 9, and front-wheel driving actuator 10 will now bedescribed.

The control device 15 further includes, as functions other than thefunctions shown in FIG. 18, a front-wheel steering actuator controlsection 41 shown in FIG. 30, a front-wheel driving actuator controlsection 42 shown in FIG. 31, and a handlebar driving actuator controlsection 43 shown in FIG. 32.

The front-wheel steering actuator control section 41 carries out drivecontrol of the front-wheel steering actuator 8, by the controlprocessing shown in the block diagram in FIG. 30, for example, to causethe actual steering angle (detected front-wheel steering angle δf_act)of the front wheel 3 f to track a desired front-wheel steering angleδf_cmd.

In this example, the front-wheel steering actuator control section 41receives a desired front-wheel steering angle δf_cmd, a desiredfront-wheel steering angular velocity δf_dot_cmd, and a desiredfront-wheel steering angular acceleration δf_dot2_cmd determined in theabove-described manner in the posture control arithmetic section 37, adetected front-wheel steering angle δf_act, and a detected front-wheelsteering angular velocity δf_dot_act which is a detected value of theactual steering angular velocity of the front wheel 3 f.

It should be noted that the detected front-wheel steering angularvelocity δf_dot_act is a value of the steering angular velocity which isrecognized on the basis of an output from the front-wheel steering angledetector 17, or a value obtained by calculating a temporal change rateof the detected front-wheel steering angle δf_act.

The front-wheel steering actuator control section 41 determines, fromthe above-described input values, an electric current command valueI_δf_cmd which is a desired value of the electric current passed throughthe front-wheel steering actuator 8 (electric motor), by the processingin an electric current command value determining section 41-1.

The electric current command value determining section 41-1 determinesthe electric current command value I_δf_cmd by summing up a feedbackmanipulated variable component obtained by multiplying a deviationδf_act from δf_cmd by a gain Kδf_p of a prescribed value, a feedbackmanipulated variable component obtained by multiplying a deviation ofδf_dot_act from δf_dot_cmd by a gain Kδf_v of a prescribed value, and afeedforward manipulated variable component obtained by multiplyingδf_dot2_cmd by a gain Kδf_a of a prescribed value, as shown by thefollowing expression (57).

$\begin{matrix}{{{I\_\delta f}{\_ cmd}} = {{{K\delta f\_ p}*\left( {{\delta f\_ cmd} - {\delta f\_ act}} \right)} + {{K\delta f\_ v}*\left( {{{\delta f\_ dot}{\_ cmd}} - {{\delta f\_ dot}{\_ act}}} \right)} + {{K\delta f\_ a}*{\delta f\_ dot2}{\_ cmd}}}} & (57)\end{matrix}$

The front-wheel steering actuator control section 41 then controls theactual electric current passed through the front-wheel steering actuator8 (electric motor) to match the electric current command value I_δf_cmd,by an electric current control section 41-2 which is made up of a motordriver or the like.

In this manner, the control is performed such that the actual steeringangle of the front wheel 3 f tracks the desired front-wheel steeringangle δf_cmd. In this case, the electric current command value I_δf_cmdincludes the third term on the right side of the above expression (57),i.e. the feedforward manipulated variable component, ensuring improvedtracking in the above-described control.

It should be noted that the technique of controlling the front-wheelsteering actuator 8 to cause the actual steering angle of the frontwheel 3 f to track the desired front-wheel steering angle δf_cmd is notlimited to the above-described technique; other techniques may be usedas well. For example, various kinds of known servo control techniquesrelated to electric motors (feedback control techniques for causing theactual angle of rotation of the rotor of the electric motor to track adesired value) may be adopted.

The front-wheel driving actuator control section 42 carries out drivecontrol of the front-wheel driving actuator 10, by the controlprocessing shown in the block diagram in FIG. 31, for example, to causethe actual rotational transfer velocity of the front wheel 3 f to tracka desired front-wheel rotational transfer velocity Vf_cmd (or to causethe actual rotational angular velocity of the front wheel 3 f to track adesired rotational angular velocity corresponding to Vf_cmd).

In this example, the front-wheel driving actuator control section 42receives a desired front-wheel rotational transfer velocity Vf_cmddetermined in the above-described manner in the desired front-wheelrotational transfer velocity determining section 36, and an estimatedfront-wheel rotational transfer velocity Vf_act.

The front-wheel driving actuator control section 42 determines, from theabove-described input values, an electric current command value I_Vf_cmdwhich is a desired value of the electric current passed through thefront-wheel driving actuator 10 (electric motor), by the processing inan electric current command value determining section 42-1.

The electric current command value determining section 42-1 determines afeedback manipulated variable component obtained by multiplying adeviation of Vf_act from Vf_cmd by a gain KVf_v of a prescribed value,as the electric current command value I_Vf_cmd, as shown by thefollowing expression (58).

I _(—) Vf _(—) cmd=KVf _(—) v*(Vf _(—) cmd−Vf_act)  (58)

It should be noted that, instead of using the above expression (58),I_Vf_cmd may be determined by, for example, multiplying a deviation ofthe detected value of the actual rotational angular velocity of thefront wheel 3 f, which is indicated by an output from the front-wheelrotational speed detector 20, from a value obtained by dividing Vf_cmdby the effective rolling radius of the front wheel 3 f (i.e. a desiredvalue of the rotational angular velocity of the front wheel 3 f) by again of a prescribed value.

The front-wheel driving actuator control section 42 then controls theactual electric current passed through the front-wheel driving actuator10 (electric motor) to match the electric current command valueI_Vf_cmd, by an electric current control section 42-2 which is made upof a motor driver or the like.

In this manner, the control is performed such that the actual rotationaltransfer velocity of the front wheel 3 f tracks the desired front-wheelrotational transfer velocity Vf_cmd (or such that the actual rotationalangular velocity tracks the desired value of the rotational angularvelocity corresponding to Vf_cmd).

It should be noted that the technique of controlling the front-wheeldriving actuator 10 to cause the actual rotational transfer velocity ofthe front wheel 3 f to track the desired front-wheel rotational transfervelocity Vf_cmd is not limited to the above-described technique; othertechniques may be used as well. For example, various kinds of knownspeed control techniques related to electric motors (feedback controltechniques for causing the actual rotational angular velocity of therotor of the electric motor to track a desired value) may be adopted.

The handlebar driving actuator control section 43 carries out drivecontrol of the handlebar driving actuator 9, by the control processingshown in the block diagram in FIG. 32, for example, to cause the actualrotational angle (handlebar angle) of the steering handlebar 7 to tracka desired handlebar angle δh_cmd.

In this example, the handlebar driving actuator control section 43receives a desired handlebar angle δh_cmd and a desired handlebarangular velocity δh_dot_cmd determined in the above-described manner inthe desired handlebar angle determining section 38, a detected handlebarangle δh_act which is a detected value of the actual rotational angle ofthe steering handlebar 7, and a detected handlebar angular velocityδh_dot_act which is a detected value of the actual rotational angularvelocity of the steering handlebar 7.

It should be noted that the detected handlebar angle δh_act and thedetected handlebar angular velocity δh_dot_act are a value of thehandlebar angle which is recognized on the basis of an output from thehandlebar angle detector 18 and a value indicating a temporal changerate thereof, respectively.

The handlebar driving actuator control section 43 determines, from theabove-described input values, an electric current command value I_δh_cmdwhich is a desired value of the electric current passed through thehandlebar driving actuator 9 (electric motor), by the processing in anelectric current command value determining section 43-1.

The electric current command value determining section 43-1 determinesthe electric current command value I_δh_cmd by summing up a feedbackmanipulated variable component obtained by multiplying a deviation ofδh_act from δh_cmd by a gain Kδh_p of a prescribed value and a feedbackmanipulated variable component obtained by multiplying a deviation ofδh_dot_act from δh_dot_cmd by a gain Kδh_v of a prescribed value, asshown by the following expression (59).

I _(—) δh _(—) cmd=Kδh _(—) p*(δh _(—) cmd−δh_act)+Kδh _(—)v*(δh_dot_(—) cmd−δh_dot_act)  (59)

The handlebar driving actuator control section 43 then controls theactual electric current passed through the handlebar driving actuator 9(electric motor) to match the electric current command value I_δh_cmd,by an electric current control section 43-2 which is made up of a motordriver or the like.

In this manner, the control is performed such that the actual handlebarangle of the steering handlebar 7 tracks the desired handlebar angleδh_cmd.

It should be noted that the technique of controlling the handlebardriving actuator 9 to cause the actual handlebar angle of the steeringhandlebar 7 to track the desired handlebar angle δh_cmd is not limitedto the above-described technique; various kinds of known servo controltechniques, for example, may be adopted.

The above has described the details of the control processing in thecontrol device 15 according the present embodiment.

Here, the correspondence between the present embodiment and the presentinvention will be described. In the present embodiment, the front wheel3 f corresponds to the steering control wheel in the present invention,and the front-wheel steering actuator 8 (electric motor) corresponds tothe steering actuator in the present invention.

Further, the inverted pendulum mass point 123 (first mass point 123) andthe second mass point 124 in the two-wheeled vehicle 1A correspondrespectively to the mass points A and B in the present invention. Thedynamic behavior of the system having the inverted pendulum mass point123 (first mass point 123) and the second mass point 124 is specificallyexpressed by the aforesaid expressions (19) to (27).

Further, in the present embodiment, for stabilizing the posture of thevehicle body 2, the front-wheel steering actuator 8 (electric motor) iscontrolled such that the inverted pendulum mass point lateral movementamount and the inverted pendulum mass point lateral velocity,constituting the motional state quantity of the inverted pendulum masspoint 123, each approach (or converge to) zero, which is the desiredvalue (Pb_diff_y_cmd, Vby_cmd), and also that the steering angle and thesteering angular velocity, constituting the motional state quantity ofthe steering angle of the steering control wheel (front wheel 3 f), eachapproach (or converge to) zero, which is the desired value.

Specifically, in the processing in the posture control arithmeticsection 37, the desired front-wheel steering angular accelerationδf_dot2_cmd as an operational target of the front-wheel steeringactuator 8 (steering actuator) is determined, by a feedback control law,so as to cause a deviation of each of the estimated inverted pendulummass point lateral movement amount Pb_diff_y_act, the estimated invertedpendulum mass point lateral velocity Vby_act, the last time's desiredfront-wheel steering angle δf_cmd_p, representing a pseudo estimate ofthe steering angle δf, and the last time's desired front-wheel steeringangular velocity δf_dot_cmd_p, representing a pseudo estimate of thesteering angular velocity δf_dot, from the corresponding desired valueto converge to zero.

Further, the driving force of the front-wheel steering actuator 8 iscontrolled by the aforesaid front-wheel steering actuator controlsection 41 such that the actual steering angle of the front wheel 3 ftracks a desired front-wheel steering angle δf_cmd which has beendetermined by performing integration twice on the above-describedδf_dot2_cmd.

In this manner; the front-wheel steering actuator 8 is controlled so asto stabilize the motional state quantity of the inverted pendulum masspoint 123 and the motional state quantity of the steering angle of thesteering control wheel (front wheel 3 f) and, hence, to stabilize theposture (in the roll direction) of the vehicle body 2.

In the present embodiment, the arrangement (relative to the front wheel3 f) of the steering axis Csf of the front wheel 3 f which is a steeringcontrol wheel is set such that, in the basic posture state of thetwo-wheeled vehicle 1A, the intersection point Ef of the steering axisCsf and a virtual straight line connecting the center of the axle of thefront wheel 3 f and the ground contact point thereof is located belowthe ground surface 110 (that is, such that the height a of theintersection point Ef from the ground surface 110 satisfies: a<0).

Therefore, the condition that a<a_sum (and, hence, the aforesaid “firstcondition” in the present invention) is naturally satisfied for a_sumdefined by the aforesaid expression (28). Further; the condition thata≦a_s (and, hence, the “second condition” in the present invention) isalso naturally satisfied for a_s defined by the aforesaid expression(40). Still further, the condition that a≦Rf is also naturally satisfiedfor the radius of curvature, Rf, of the transverse cross-sectional shapeof the steering control wheel (front wheel 3 f) in the basic posturestate of the two-wheeled vehicle 1A.

According to the present embodiment described above, it is set suchthat, in the basic posture state of the two-wheeled vehicle 1A, theheight a of the intersection point Ef of the steering axis Csf of thefront wheel 3 f which is a steering control wheel and a virtual straightline connecting the center of the axle of the front wheel 3 f and theground contact point thereof satisfies: a<0 (and, hence, a<a_aum, a≦a_s,a≦Rf), as described above. As a result, the height a is set to satisfythe aforesaid “first condition” and “second condition”.

Therefore, in the case where the actual inverted pendulum mass pointlateral movement amount (estimated inverted pendulum mass point lateralmovement amount Pb_diff_y_act) of the two-wheeled vehicle 1A deviatesfrom the desired inverted pendulum mass point lateral movement amountPb_diff_y_cmd (in other words, in the case where the actual posture ofthe vehicle body 2 deviates from the desired posture satisfyingPb_diff_y_act=0), the steering of the front wheel 3 f by the drivingforce of the front-wheel steering actuator 8 can cause a moment (in theroll direction) capable of making the actual inverted pendulum masspoint lateral movement amount of the two-wheeled vehicle 1A smoothlyrestored to the desired inverted pendulum mass point lateral movementamount Pb_diff_y_cmd to act on the vehicle body 2, without the need forthe rider to intentionally move the steering handlebar 7. That is, it ispossible to cause the moment in the roll direction for stabilizing theposture of the vehicle body 2 to act on the vehicle body 2.

According to this moment, the actual roll angle of the vehicle body 2 ischanged, so that the actual inverted pendulum mass point lateralmovement amount is restored to the desired inverted pendulum mass pointlateral movement amount Pb_diff_y_cmd. It should be noted that theactual inverted pendulum mass point lateral movement amount beingrestored to the desired inverted pendulum mass point lateral movementamount Pb_diff_y_cmd more specifically means that the actual roll angleof the vehicle body 2 and the actual steering angle of the front wheel 3f are controlled so as to cause the estimated inverted pendulum masspoint lateral movement amount Pb_diff_y_act, calculated by the aforesaidexpression (51) from the actual roll angle of the vehicle body 2 and theactual steering angle of the front wheel 3 f, to match the desiredinverted pendulum mass point lateral movement amount Pb_diff_y_cmd.

At this time, the sensitivity of the above-described moment generated inaccordance with the change in steering angle of the front wheel 3 f isrelatively high. Therefore, the actual inverted pendulum mass pointlateral movement amount of the two-wheeled vehicle 1A can be restored tothe desired inverted pendulum mass point lateral movement amountPb_diff_y_cmd, without causing an excessive change in steering angle ofthe front wheel 3 f.

Further, through calculation of the desired front-wheel steering angularacceleration δf_dot2_cmd by the aforesaid expression (55), the desiredfront-wheel steering angular acceleration δf_dot2_cmd (operationaltarget of the front-wheel steering actuator 8) is determined to make adeviation (Pb_diff_y_cmd−Pb_diff_y_act) of the estimated invertedpendulum mass point lateral movement amount Pb_diff_y_act, representingan observed value of the current actual inverted pendulum mass pointlateral movement amount, from the desired inverted pendulum mass pointlateral movement amount Pb_diff_y_cmd of the two-wheeled vehicle 1A, adeviation (Vby_cmd−Vby_act) of the estimated inverted pendulum masspoint lateral velocity Vby_act, representing an observed value of thecurrent actual inverted pendulum mass point lateral velocity, from thedesired inverted pendulum mass point lateral velocity Vby_cmd of thetwo-wheeled vehicle 1A, the last time's desired front-wheel steeringangle δf_cmd_p, representing a pseudo estimate of the current actualsteering angle (from the neutral steering angle) of the front wheel 3 f,and the last time's desired front-wheel steering angular velocityδf_dot_cmd_p, representing a pseudo estimate of the angular velocity ofthe current actual steering angle of the front wheel 3 f, each approach“0” in the state where the rider is not attempting to move the steeringhandlebar 7.

Therefore, the steering angle of the front wheel 3 f is controlled so asto cause the actual inverted pendulum mass point lateral movement amountand inverted pendulum mass point lateral velocity to converge to therespective desired values (zero in the present embodiment), whilepreventing the actual steering angle of the front wheel 3 f fromdiverging from the neutral steering angle (while causing the actualsteering angle to ultimately converge to the neutral steering angle).

Accordingly, the posture of the vehicle body 2 can be stabilizedsmoothly, particularly when the two-wheeled vehicle 1A is stopped ortraveling at a low speed. Further, the two-wheeled vehicle 1A can bestarted smoothly with the vehicle body 2 in a stable posture.

In the case where a rider applies a rotative force (about the handlebaraxis Ch) to the steering handlebar 7 in an attempt to move the steeringhandlebar 7, the steering angle of the front wheel 3 f can be controlledwith an angular acceleration corresponding to the magnitude of therotative force applied to the steering handlebar 7, by the feedforwardmanipulated variable Th_act*Kh.

Further, the gains K1 and K2, which are the feedback gains related tothe posture control in the roll direction of the vehicle body 2, arevariably determined, as described above, in accordance with theestimated traveling speed Vox_act, which is an observed value of thecurrent actual traveling speed (transfer velocity in the X-axisdirection) of the two-wheeled vehicle 1A, and the last time's desiredfront-wheel steering angle δf_cmd_p, which is a pseudo estimate of thecurrent actual steering angle of the front wheel 3 f. Further, the gainsK3 and K4, which are the feedback gains related to the control of thesteering angle of the front wheel 3 f, are variably determined, asdescribed above, in accordance with the estimated traveling speedVox_act.

Accordingly, when the two-wheeled vehicle 1A is stopped or traveling ata low speed, it is possible to perform the steering of the front wheel 3f to cause the actual inverted pendulum mass point lateral movementamount of the two-wheeled vehicle 1A to quickly approach the desiredinverted pendulum mass point lateral movement amount Pb_diff_y_cmd.

In the state where the two-wheeled vehicle 1A is traveling at a highspeed, the steering angle of the front wheel 3 f can readily bemaintained at the neutral steering angle. Further, even if the vehiclebody 2 is leaned, the steering control of the front wheel 3 f forcausing the actual inverted pendulum mass point lateral movement amountof the two-wheeled vehicle 1A to approach the desired inverted pendulummass point lateral movement amount Pb_diff_y_cmd is not performed, orsuch steering control is restricted. Consequently, a rider can readilyturn the two-wheeled vehicle 1A by banking the vehicle body 2 byshifting the weight of the rider's body, as with a conventionaltwo-wheeled vehicle.

Second Embodiment

A second embodiment of the present invention will be described belowwith reference to FIGS. 33 to 45.

Referring to FIG. 33, a mobile vehicle 201A according to the presentembodiment is a two-wheeled vehicle embodying the rear-wheel steeringtwo-wheeled vehicle 201 shown in FIG. 11. In the description of thepresent embodiment, for convenience sake, the components of the mobilevehicle 201A having the same functions as those of the rear-wheelsteering two-wheeled vehicle 201 shown in FIG. 11 will be denoted by thesame reference signs as those used in FIG. 11.

This mobile vehicle 201A (hereinafter, referred to as “two-wheeledvehicle 201A”) has a vehicle body 202, and a front wheel 203 f and arear wheel 203 r arranged spaced apart from each other in thelongitudinal direction of the vehicle body 202.

On the upper surface of the vehicle body 202, a seat 206 is provided fora rider to sit astride.

At the front portion of the vehicle body 202, a front-wheel supportmechanism 204 for axially supporting the front wheel 203 f, and asteering handlebar 207 for a rider who has sat on the seat 206 to holdare mounted.

The front-wheel support mechanism 204 is made up of a front fork whichincludes a suspension mechanism such as a damper, for example. Themechanical structure of the front-wheel support mechanism is similar tothat of a conventional motorcycle, for example. At one end of thisfront-wheel support mechanism 204 (at its end on the front side of thevehicle body 202), the front wheel 203 f is axially supported, viabearings or the like, such that it can rotate about the axle centerlineCf (rotational axis of the front wheel 203 f) that extends in thedirection orthogonal to the diameter direction of the front wheel 203 f(in the direction perpendicular to the paper plane of FIG. 33).

The front-wheel support mechanism 204 is mounted to the front portion ofthe vehicle body 202 such that the mechanism can rotate about a steeringaxis Csf which is tilted backward. This configuration makes the frontwheel 203 f serve as a steering control wheel which can be rotated, or,steered about the steering axis Csf together with the front-wheelsupport mechanism 204.

The steering handlebar 207 is mounted to the front portion of thevehicle body 202 so as to be able to rotate about the steering axis Csfof the front wheel 203 f in an integrated manner with the front-wheelsupport mechanism 204. Although not shown in detail in the figure, thissteering handlebar 207 is equipped with an accelerator grip, brakelever, turn signal switch, and so on, as with the handlebar of aconventional motorcycle.

The rear portion of the vehicle body 202 is extended to over the rearwheel 203 r. At the rear end portion of the vehicle body 202, arear-wheel support mechanism 205 for axially supporting the rear wheel203 r in a rotatable manner and an actuator 208 for generating a drivingforce for steering the rear wheel 203 r are mounted.

The rear-wheel support mechanism 205 is made up of a suspensionmechanism including a damper and a swing arm. The rear-wheel supportmechanism 205 is arranged to extend downward from the rear end portionof the vehicle body 202.

At the lower end of the rear-wheel support mechanism 205, the rear wheel203 r is axially supported, via bearings or the like, such that it canrotate about the axle centerline Cr (rotational axis of the rear wheel203 r) that extends in the direction orthogonal to the diameterdirection of the rear wheel 203 r (in the direction perpendicular to thepaper plane of FIG. 33).

In the present embodiment, an actuator 209 for rotatively driving therear wheel 203 r about its axle centerline Cr is attached to the axle ofthe rear wheel 203 r. The actuator 209 serves as a power engine whichgenerates a thrust force for the two-wheeled vehicle 201A. In thepresent embodiment, this actuator 209 (hereinafter, also referred to as“rear-wheel driving actuator 209”) is made up of an electric motor (witha speed reducer).

It should be noted that the actuator 209 may be made up of a hydraulicactuator, for example, instead of the electric motor. Alternatively, theactuator 209 may be made up of an internal combustion engine.Furthermore, the actuator 209 may be attached to the vehicle body 202 ata position apart from the axle of the rear wheel 203 r, and the actuator209 and the axle of the rear wheel 203 r may be connected by anappropriate power transmission device.

The rear-wheel support mechanism 205 is mounted to the vehicle body 202such that the mechanism can rotate about a steering axis Csr which istilted backward. This configuration makes the rear wheel 203 r serve asa steering control wheel which can be rotated, or, steered about thesteering axis Csr together with the rear-wheel support mechanism 205. Asthe steering axis Csr is tilted backward, the rear wheel 203 r has apositive caster angle θcr.

In this case, in the two-wheeled vehicle 201A of the present embodiment,the relative arrangement of the steering axis Csr and the rear wheel 203r in the basic posture state of the vehicle is set, as shown in FIG. 33,such that an intersection point Er′ of the steering axis Csr and astraight line connecting the center of the axle of the rear wheel 203 rand the ground contact point thereof is located below the ground surface110 in the basic posture state. Accordingly, a height a′ of theintersection point Er′ from the ground surface 110 takes a negativevalue.

It should be noted that the basic posture state of the two-wheeledvehicle 201A is, as with the basic posture state of the two-wheeledvehicle 201 in FIG. 11, the state where the front wheel 203 f and therear wheel 203 r are both stationary in the upright posture in contactwith the ground surface 110 and the axle centerlines (centers of therotational axes) Cf and Cr of the front wheel 203 f and the rear wheel203 r extend in parallel with each other in the direction orthogonal tothe longitudinal direction of the vehicle body 202.

The aforesaid actuator 208 generates, as a driving force for performingthe steering of the rear wheel 203 r, a rotative driving force to causethe rear wheel 203 r to rotate about the steering axis Csr. In thepresent embodiment, this actuator 208 is made up of an electric motor(with a speed reducer). The actuator 208 (hereinafter, also referred toas “rear-wheel steering actuator 208”) is connected to the rear-wheelsupport mechanism 205 so as to apply the rotative driving force aboutthe steering axis Csr to the rear-wheel support mechanism 205.

Accordingly, as the rotative driving force is applied from therear-wheel steering actuator 208 to the rear-wheel support mechanism205, the rear-wheel support mechanism 205 is rotatively driven about thesteering axis Csr together with the rear wheel 203 r. As a result, therear wheel 203 r is steered by the rotative driving force from therear-wheel steering actuator 208.

It should be noted that the actuator 208 is not limited to the electricmotor; it may be made up, for example, of a hydraulic actuator.

Besides the above-described mechanical configuration, the two-wheeledvehicle 201A includes, as shown in FIG. 34, a control device 215 whichcarries out control processing for controlling the operations of therear-wheel steering actuator 208 and the rear-wheel driving actuator 209(and, hence, controlling the posture of the vehicle body 202 and so on).

The two-wheeled vehicle 201A further includes, as sensors for detectingvarious kinds of state quantities necessary for the control processingin the control device 215, a vehicle-body inclination detector 216 fordetecting an inclination angle φb in the roll direction of the vehiclebody 202, a front-wheel steering angle detector 217 for detecting asteering angle δf (angle of rotation about the steering axis Csf) of thefront wheel 203 f, a rear-wheel steering angle detector 218 fordetecting a steering angle or (angle of rotation about the steering axisCsr) of the rear wheel 203 r, a front-wheel rotational speed detector219 for detecting a rotational speed (angular velocity) of the frontwheel 203 f, a rear-wheel rotational speed detector 220 for detecting arotational speed (angular velocity) of the rear wheel 203 r, and anaccelerator manipulation detector 221 which outputs a detection signalcorresponding to the manipulated variable (rotational amount) of theaccelerator grip of the steering handlebar 207.

It should be noted that the steering angle δr of the rear wheel 203 rmore specifically means the rotational angle of the rear wheel 203 rfrom the steering angle (neutral steering angle) in its non-steeredstate (the state in which the direction of the axle centerline Cr of therear wheel 203 r corresponds to the direction orthogonal to thelongitudinal direction of the vehicle body 202 (or, direction parallelto the Y axis)). Therefore, the steering angle δr of the rear wheel 203r in the non-steered state is “0”. The same applies to the steeringangle δf the front wheel 203 f.

The positive rotational direction of the steering angle δr of the rearwheel 203 r corresponds to the direction of rotation that makes thefront end of the rear wheel 203 r turn left with respect to the vehiclebody 202 (in other words, the direction in which the rear wheel 203 rturns counterclockwise about the steering axis Csr as the two-wheeledvehicle 201A is seen from above), as in the case of the two-wheeledvehicle 201 shown in FIG. 11. The same applies to the steering angle δfof the front wheel 203 f.

The control device 215, which is an electronic circuit unit made up of aCPU, RAM, ROM, interface circuit and so on, is mounted on the vehiclebody 202. This control device 215 is configured to receive outputs(detection signals) from the respective detectors 216 to 221 describedabove.

The control device 215 may include a plurality of CPUs or processors.Further, the control device 215 may be made up of a plurality ofmutually communicable electronic circuit units.

The vehicle-body inclination detector 216, which is made up of anacceleration sensor and a gyro sensor (angular velocity sensor), forexample, is mounted on the vehicle body 202. In this case, the controldevice 215 carries out arithmetic processing on the basis of the outputsof the acceleration sensor and the gyro sensor to measure theinclination angle in the roll direction (more specifically, theinclination angle in the roll direction with respect to the verticaldirection (direction of gravitational force)) of the vehicle body 202.For this measurement, the technique proposed by the present applicant inJapanese Patent No. 4181113, for example, may be adopted.

The front-wheel steering angle detector 217 is made up, for example, ofa rotary encoder attached to the rotary shaft of the front-wheel supportmechanism 204 (or the steering handlebar 207) on the aforesaid steeringaxis Csf.

The rear-wheel steering angle detector 218 is made up, for example, of arotary encoder attached to the rear-wheel steering actuator 208 on theaforesaid steering axis Csr.

The front-wheel rotational speed detector 219 is made up, for example,of a rotary encoder attached to the axle of the front wheel 203 f.

The rear-wheel rotational speed detector 220 is made up, for example, ofa rotary encoder attached to the axle of the rear wheel 203 r.

The accelerator manipulation detector 221 is made up, for example, of arotary encoder or a potentiometer built in the steering handlebar 207.

The functions of the above-described control device 215 will bedescribed further with reference to FIG. 35. The XYZ coordinate systemused in the following description is, as in the case of the two-wheeledvehicle 201 in FIG. 11, a coordinate system in which, in the basicposture state of the two-wheeled vehicle 201A, the vertical direction(up-and-down direction) is defined as the Z-axis direction, thelongitudinal direction of the vehicle body 202 as the X-axis direction,the lateral direction of the vehicle body 202 as the Y-axis direction,and a point on the ground surface 110 immediately beneath the overallcenter of gravity G of the two-wheeled vehicle 201A as the origin (seeFIG. 33).

The control device 215 includes, as functions implemented when the CPUexecutes installed programs (functions implemented by software) or asfunctions implemented by hardware, as shown in FIG. 35: an estimatedinverted pendulum mass point lateral movement amount calculating section231 which calculates an estimate of an actual value Pb_diff_y_act(hereinafter, referred to as “estimated inverted pendulum mass pointlateral movement amount Pb_diff_y_act”) of an inverted pendulum masspoint lateral movement amount Pb_diff_y representing a movement amountin the Y-axis direction (lateral direction of the vehicle body 202) ofan inverted pendulum mass point 123 (=first mass point 123) of thetwo-wheeled vehicle 201A, an estimated inverted pendulum mass pointlateral velocity calculating section 232 which calculates an estimate ofan actual value Vby_act (hereinafter, referred to as “estimated invertedpendulum mass point lateral velocity Vby_act”) of an inverted pendulummass point lateral velocity Vby representing a translational velocity inthe Y-axis direction (lateral direction of the vehicle body 202) of theinverted pendulum mass point 123, an estimated traveling speedcalculating section 233 which calculates an estimate of the actual valueVox_act (hereinafter, referred to as “estimated traveling speedVox_act”) of the traveling speed Vox of the two-wheeled vehicle 201A, adesired posture state determining section 234 which determines a desiredvalue Pb_diff_y_cmd (hereinafter, referred to as “desired invertedpendulum mass point lateral movement amount Pb_diff_y_cmd”) of theinverted pendulum mass point lateral movement amount Pb_diff_y and adesired value Vby_cmd (hereinafter, referred to as “desired invertedpendulum mass point lateral velocity Vby_cmd”) of the inverted pendulummass point lateral velocity Vby, a control gain determining section 235which determines values of a plurality of gains K1, K2, K3, and K4 forposture control of the vehicle body 202, and a desired rear-wheelrotational transfer velocity determining section 236 which determines adesired value Vr_cmd (hereinafter, referred to as “desired rear-wheelrotational transfer velocity Vr_cmd”) of the rotational transfervelocity Vr of the rear wheel 203 r (translational velocity of the rearwheel 203 r as the rear wheel 203 r rolls on the ground surface 110).

The control device 215 further includes a posture control arithmeticsection 237 which carries out arithmetic processing for the posturecontrol of the vehicle body 202 to thereby determine a desired valueδr_cmd (hereinafter, referred to as “desired rear-wheel steering angleδr_cmd”) of the steering angle δr of the rear wheel 203 r, a desiredvalue δr_dot_cmd (hereinafter, referred to as “desired rear-wheelsteering angular velocity δr_dot_cmd”) of the steering angular velocityδr_dot which is a temporal change rate of the steering angle δr, and adesired value δr_dot2_cmd (hereinafter, referred to as “desiredrear-wheel steering angular acceleration δr_dot2_cmd”) of the steeringangular acceleration δr_dot2 which is a temporal change rate of thesteering angular velocity δr_dot.

The control device 215 carries out the processing in the above-describedfunctional sections successively at prescribed control processingcycles. The control device 215 then controls the rear-wheel steeringactuator 208 in accordance with the desired rear-wheel steering angleδr_cmd, the desired rear-wheel steering angular velocity δr_dot_cmd, andthe desired rear-wheel steering angular acceleration δr_dot2_cmddetermined by the posture control arithmetic section 237.

Further, the control device 215 controls the rear-wheel driving actuator209 in accordance with the desired rear-wheel rotational transfervelocity Vr_cmd determined by the desired rear-wheel rotational transfervelocity determining section 236.

The control processing performed by the control device 215 will bedescribed below in detail.

At each control processing cycle, the control device 215 first carriesout the processing in the estimated inverted pendulum mass point lateralmovement amount calculating section 231. It should be noted that thealgorithm of the processing in the estimated inverted pendulum masspoint lateral movement amount calculating section 231 in the presentembodiment has been established assuming, by way of example, that thedynamic behavior of the two-wheeled vehicle 201A is expressed by thedynamic behavior that is obtained when the system in which a mass pointand an inertia moment have been set only for the vehicle body 202 of thetwo-wheeled vehicle 201A, as in the two-wheeled vehicle 201 in FIG. 11,is equivalently transformed to the system, shown in FIG. 2B, which ismade up of the aforesaid first mass point 123 (inverted pendulum masspoint) and the second mass point 124.

As shown in FIG. 35, the estimated inverted pendulum mass point lateralmovement amount calculating section 231 receives a detected value of theactual value φb_act (hereinafter, referred to as “detected roll angleφb_act”) of the roll angle (inclination angle in the direction about theX axis (roll direction)) φb of the vehicle body 202, a detected value ofthe actual value δf_act (hereinafter, referred to as “detectedfront-wheel steering angle δf_act”) of the steering angle δf the frontwheel 203 f, and a detected value of the actual value δr_act(hereinafter, referred to as “detected rear-wheel steering angleδr_act”) of the steering angle δr of the rear wheel 203 r.

The detected roll angle φb_act is a detected value (observed value)indicated by an output from the vehicle-body inclination detector 216,the detected front-wheel steering angle δf_act is a detected value(observed value) indicated by an output from the front-wheel steeringangle detector 217, and the detected rear-wheel steering angle δr_act isa detected value (observed value) indicated by an output from therear-wheel steering angle detector 218.

Here, in the case where it is assumed that a mass point and an inertiamoment are set only for the vehicle body 202 of the two-wheeled vehicle201A and that the dynamic behavior of the two-wheeled vehicle 201A isexpressed by the behavior of the mass point system made up of the firstmass point 123 (inverted pendulum mass point) and the second mass point124, the first mass point 123 and the second mass point 124 are on theplane of symmetry of the vehicle body 202 (plane of symmetry when thevehicle body 202 is considered to be bilaterally symmetrical), asexplained above. Therefore, the inclination in the roll direction of theline segment connecting the first mass point 123 and the second masspoint 124 corresponds to the inclination in the roll direction of thevehicle body 202 of the two-wheeled vehicle 201A.

Accordingly, in the case where the inclination angle φb in the rolldirection of the vehicle body 202 of the two-wheeled vehicle 201A issufficiently small, the difference between the movement amount in theY-axis direction of the first mass point 123 and the movement amount inthe Y-axis direction of the second mass point 124 coincides with a valueobtained by multiplying the inclination angle φb in the roll directionof the vehicle body 202 of the two-wheeled vehicle 201A by the height h′of the first mass point 123.

Further, in the two-wheeled vehicle 201A of the present embodiment, thefront wheel 203 f and the rear wheel 203 r are both steering controlwheels. Therefore, the movement amount q in the Y-axis direction of thesecond mass point 124 is determined uniquely from the steering angle 3 fof the front wheel 3 f and the steering angle or of the rear wheel 203r.

Accordingly, the movement amount in the Y-axis direction of the firstmass point 123, which is the inverted pendulum mass point, is obtainedas a sum of a component attributable to the inclination in the rolldirection of the vehicle body 202 of the two-wheeled vehicle 201A, acomponent attributable to the steering angle δf the front wheel 203 f,and a component attributable to the steering angle δr of the rear wheel203 r.

The estimated inverted pendulum mass point lateral movement amountcalculating section 231 uses this relationship to calculate theestimated inverted pendulum mass point lateral movement amountPb_diff_y_act on the basis of the detected roll angle φb_act, thedetected front-wheel steering angle δf_act, and the detected rear-wheelsteering angle δr_act.

More specifically, the estimated inverted pendulum mass point lateralmovement amount calculating section 231 calculates the estimatedinverted pendulum mass point lateral movement amount Pb_diff_y_act bythe processing shown in the block diagram in FIG. 36.

This processing is configured to sum up a first estimated lateralmovement amount component Pb_diff_y_act_(—)1, which is an estimate ofthe actual movement amount in the Y-axis direction of the invertedpendulum mass point 123 caused by the inclination in the roll directionof the vehicle body 202, a second estimated lateral movement amountcomponent Pb_diff_y_act_(—)2, which is an estimate of the actualmovement amount in the Y-axis direction of the inverted pendulum masspoint 123 caused by the steering of the front wheel 203 f, and a thirdestimated lateral movement amount component Pb_diff_y_act_(—)3, which isan estimate of the actual movement amount in the Y-axis direction of theinverted pendulum mass point 123 caused by the steering of the rearwheel 203 r, to thereby calculate the estimated inverted pendulum masspoint lateral movement amount Pb_diff_y_act.

In FIG. 36, a processing section 231-1 represents a processing sectionwhich obtains the first estimated lateral movement amount componentPb_diff_y_act_(—)1, a processing section 231-2 represents a processingsection which obtains the second estimated lateral movement amountcomponent Pb_diff_y_act_(—)2, a processing section 231-3 represents aprocessing section which obtains the third estimated lateral movementamount component Pb_diff_y_act_(—)3, and a processing section 231-4represents a processing section which sums up the first estimatedlateral movement amount component Pb_diff_y_act_(—)1, the secondestimated lateral movement amount component Pb_diff_y_act_(—)2, and thethird estimated lateral movement amount component Pb_diff_y_act_(—)3.

The processing section 231-1 determines the first estimated lateralmovement amount component Pb_diff_y_act_(—)1 in accordance with thedetected roll angle φb_act at the current time. More specifically, theprocessing section 231-1 multiplies the detected roll angle φb_act(angle value in [rad]) by the height h′ (=c+h), multiplied by −1, of theinverted pendulum mass point 123, to calculate the first estimatedlateral movement amount component Pb_diff_y_act_(—)1 (=φb_act*(−h′)).

Accordingly, the first estimated lateral movement amount componentPb_diff_y_act_(—)1 is calculated, in accordance with the detected rollangle φb_act, as a value of a linear function with respect to the rollangle φb of the vehicle body 202 (a value of a constant multiple of(φb). Further, Pb_diff_y_act_(—)1 becomes zero in the state whereφb_act=0 (where the vehicle body 202 is not leaned to the right orleft), and therefore, it is the movement amount in the Y-axis directionwith reference to the position of the inverted pendulum mass point 123in that state.

It should be noted that sin(φb_act) is approximated by φb_act in thecalculating processing in the processing section 231-1. Further, thevalue of h′ (or c, h) has been preset in the two-wheeled vehicle 201Aand is stored in a memory in the control device 215. For example, thevalue has been set to satisfy the relationship in the aforesaidexpression (5b) (the relationship that c(=h′−h)=I/(m*h)), from theheight h of the overall center of gravity G in the basic posture stateof the two-wheeled vehicle 201A, the overall inertia I of thetwo-wheeled vehicle 201A (inertia moment about the axis passing throughthe overall center of gravity G and parallel to the X-axis direction),and the total mass m of the two-wheeled vehicle 201A.

The value of h′, however, may be set to a value roughly approximatingthe value satisfying the relationship in the above expression (5b) suchthat optimal control characteristics can be obtained on the basis ofvarious experiments, simulation, etc.

The processing section 231-2 in FIG. 36 determines the second estimatedlateral movement amount component Pb_diff_y_act_(—)2 in accordance withthe detected front-wheel steering angle δf_act at the current time. Morespecifically, the processing section 231-2 obtains the second estimatedlateral movement amount component Pb_diff_y_act_(—)2 (=Plfy(δf_act))from the detected front-wheel steering angle δf_act at the current time,by a preset conversion function Plfy(δf). That is, the processingsection 231-2 obtains a value Plfy(δf_act) of the conversion functionPlfy(δf) corresponding to δf_act, and determines the obtained value asthe second estimated lateral movement amount componentPb_diff_y_act_(—)2.

The above conversion function Plfy(δf) is defined, for example, by amapping or an arithmetic expression. The conversion function Plfy(δf) isa nonlinear function which has been preset, as illustrated by the graphshown in the processing section 231-2 in FIG. 36, such that Plfy(δf)monotonically changes (in the present embodiment, monotonicallyincreases) with increasing steering angle δf of the front wheel 203 f,and such that the magnitude of the rate of change of Plfy(δf) withrespect to the steering angle δf (the amount of change of Plfy(δf) perunit increase of δf) becomes relatively small in the region where themagnitude (absolute value) of the steering angle δf the front wheel 203f is relatively large, compared to that in the region where themagnitude of the steering angle δf is small (region where δf is nearzero).

Accordingly, the second estimated lateral movement amount componentPb_diff_y_act_(—)2 is determined, in accordance with the detectedfront-wheel steering angle δf_act, as a value of a nonlinear functionwith respect to the steering angle δf the front wheel 203 f.

The processing section 231-3 in FIG. 36 determines the third estimatedlateral movement amount component Pb_diff_y_act_(—)3 in accordance withthe detected rear-wheel steering angle δr_act at the current time. Morespecifically, the processing section 231-3 obtains the third estimatedlateral movement amount component Pb_diff_y_act_(—)3 (=Plry(Or act))from the detected rear-wheel steering angle δr_act at the current time,by a preset conversion function Plry(δr). That is, the processingsection 231-3 obtains a value Plry(δr_act) of the conversion functionPlry(δr) that corresponds to δr_act, and determines the obtained valueas the third estimated lateral movement amount componentPb_diff_y_act_(—)3.

The conversion function Plry(δr) is defined, for example, by a mappingor an arithmetic expression. The conversion function Plry(δr) is anonlinear function which has been preset, as illustrated by the graphshown in the processing section 231-3 in FIG. 36, such that Plry(δr)monotonically changes (in the present embodiment, monotonicallydecreases) with increasing steering angle δr of the rear wheel 203 r,and such that the magnitude of the rate of change of Plry(δr) withrespect to the steering angle δr (the amount of change of Plry(δr) perunit increase of δr) becomes relatively small in the region where themagnitude (absolute value) of the steering angle δr of the rear wheel203 r is relatively large, compared to that in the region where themagnitude of the steering angle δr is small (region where δr is nearzero).

Accordingly, the third estimated lateral movement amount componentPb_diff_y_act_(—)3 is determined, in accordance with the detectedrear-wheel steering angle δr_act, as a value of a nonlinear functionwith respect to the steering angle δr of the rear wheel 203 r.

The estimated inverted pendulum mass point lateral movement amountcalculating section 231 determines the estimated inverted pendulum masspoint lateral movement amount Pb_diff_y_act by summing up, in theprocessing section 231-4, the first estimated lateral movement amountcomponent Pb_diff_y_act_(—)1, the second estimated lateral movementamount component Pb_diff_y_act_(—)2, and the third estimated lateralmovement amount component Pb_diff_y_act_(—)3 calculated in theabove-described manner.

Accordingly, the estimated inverted pendulum mass point lateral movementamount Pb_diff_y_act is determined by the following expression (71).

$\begin{matrix}\begin{matrix}{{{Pb\_ diff}{\_ y}{\_ act}} = {{{Pb\_ diff}{\_ y}{\_ act}\_ 1} + {{Pb\_ diff}{\_ y}{\_ act}\_ 2} +}} \\{{{Pb\_ diff}{\_ y}{\_ act}\_ 3}} \\{= {{{\varphi b\_ act}*\left( {- h^{\prime}} \right)} + {{Plfy}({\delta f\_ act})} + {{Plry}({\delta r\_ act})}}}\end{matrix} & (71)\end{matrix}$

In the above expression (71), the first term on the right side is alinear term with respect to the detected roll angle φb_act, the secondterm on the right side is a nonlinear term with respect to the detectedfront-wheel steering angle δf_act, and the third term on the right sideis a nonlinear term with respect to the detected rear-wheel steeringangle δr_act.

It should be noted that the second term on the right side of theexpression (71) can be ignored when the magnitude of the valuePlfy(δf_act) of the aforesaid conversion function Plfy(δf) correspondingto the actual steering angle δf_act of the front wheel 203 f issufficiently small (when the magnitude of δf_act is small).

Similarly, the third term on the right side of the expression (71) canbe ignored when the magnitude of the value Plry(δr_act) of the aforesaidconversion function Plry(δr) corresponding to the actual steering angleδr_act of the rear wheel 203 r is sufficiently small (when the magnitudeof δr_act is small).

Further, in the case where the magnitudes of both of Plfy(δf_act) andPlry(δr_act) are sufficiently small, the detected roll angle φb_act ofthe vehicle body 202 may be used instead of the estimated invertedpendulum mass point lateral movement amount Pb_diff_y_act. With thisconfiguration, the processing in the estimated inverted pendulum masspoint lateral movement amount calculating section 231 becomesunnecessary, so that the computational load of the control device 215can be reduced.

Next, the control device 215 carries out the processing in the estimatedinverted pendulum mass point lateral velocity calculating section 232.

As shown in FIG. 35, the estimated inverted pendulum mass point lateralvelocity calculating section 232 receives the estimated invertedpendulum mass point lateral movement amount Pb_diff_y_act calculated inthe estimated inverted pendulum mass point lateral movement amountcalculating section 231, a detected front-wheel steering angle δf_act,an estimate of the actual value Vf_act (hereinafter, referred to as“estimated front-wheel rotational transfer velocity Vf_act”) of therotational transfer velocity Vf of the front wheel 203 f, a detectedrear-wheel steering angle δr_act, and an estimate of the actual valueVr_act (hereinafter, referred to as “estimated rear-wheel rotationaltransfer velocity Vr_act”) of the rotational transfer velocity Vr of therear wheel 203 r.

It should be noted that the estimated front-wheel rotational transfervelocity Vf_act is a velocity which is calculated by multiplying adetected value (observed value) of the rotational angular velocity ofthe front wheel 203 f, indicated by an output from the aforesaidfront-wheel rotational speed detector 219, by a predetermined effectiverolling radius of the front wheel 203 f. Similarly, the estimatedrear-wheel rotational transfer velocity Vr_act is a velocity which iscalculated by multiplying a detected value (observed value) of therotational angular velocity of the rear wheel 203 r, indicated by anoutput from the aforesaid rear-wheel rotational speed detector 220, by apredetermined effective rolling radius of the rear wheel 203 r.

The estimated inverted pendulum mass point lateral velocity calculatingsection 232 carries out the processing shown in the block diagram inFIG. 37 to calculate an estimated inverted pendulum mass point lateralvelocity Vby_act.

This processing is configured to sum up a first estimated lateralvelocity component Vby_act_(—)1, which is an estimate of the actualtransfer velocity (relative to the origin) in the Y-axis direction ofthe inverted pendulum mass point 123 as seen from the origin of the XYZcoordinate system set in the above-described manner for the two-wheeledvehicle 201A, a second estimated lateral velocity componentVby_act_(—)2, which is an estimate of the actual transfer velocity inthe Y-axis direction of the inverted pendulum mass point 123 (=transfervelocity of the origin of the XYZ coordinate system) caused by thetranslational movement of the two-wheeled vehicle 201A accompanying therolling of the front wheel 203 f while the front wheel 203 f is beingsteered (when the actual steering angle of the front wheel 203 f is not“0”), and a third estimated lateral velocity component Vby_act_(—)3,which is an estimate of the actual transfer velocity in the Y-axisdirection of the inverted pendulum mass point 123 (=transfer velocity ofthe origin of the XYZ coordinate system) caused by the translationalmovement of the two-wheeled vehicle 201A accompanying the rolling of therear wheel 203 r while the rear wheel 203 r is being steered (when theactual steering angle of the rear wheel 203 r is not “0”), to therebycalculate the estimated inverted pendulum mass point lateral velocityVby_act.

In FIG. 37, a processing section 232-1 represents a processing sectionwhich obtains the first estimated lateral velocity componentVby_act_(—)1, a processing section 232-2 represents a processing sectionwhich obtains the second estimated lateral velocity componentVby_act_(—)2, a processing section 232-3 represents a processing sectionwhich obtains the third estimated lateral velocity componentVby_act_(—)3, and a processing section 232-4 represents a processingsection which sums up the first estimated lateral velocity componentVby_act_(—)1, the second estimated lateral velocity componentVby_act_(—)2, and the third estimated lateral velocity componentVby_act_(—)3.

The processing section 232-1 calculates, as the first estimated lateralvelocity component Vby_act_(—)1, a temporal change ratePb_diff_y_dot_act (amount of change per unit time) at the current timeof the estimated inverted pendulum mass point lateral movement amountPb_diff_y_act successively calculated by the estimated inverted pendulummass point lateral movement amount calculating section 231. That is, theprocessing section 232-1 calculates a differential valuePb_diff_y_dot_act of Pb_diff_y_act, as Vby_act_(—)1.

Further, the processing section 232-2 multiplies, in a processingsection 232-2-1, a detected front-wheel steering angle δf_act at thecurrent time by a cosine value cos(θcf) of the caster angle θcf of thefront wheel 203 f, to thereby calculate an estimate of the actual valueδ′f_act (hereinafter, referred to as “estimated front-wheel effectivesteering angle δ′f_act”) of a front-wheel effective steering angle δ′fwhich corresponds to the rotational angle in the yaw direction of thefront wheel 203 f.

Supplementally, the front-wheel effective steering angle δ′f is an angleof the line of intersection of the ground surface 110 and the rotationalplane of the front wheel 203 f being steered (plane passing through thecenter of the axle of the front wheel 203 f and orthogonal to the axlecenterline Cf thereof) with respect to the longitudinal direction(X-axis direction) of the vehicle body 202.

In the case where the roll angle φb of the vehicle body 202 isrelatively small, the estimated front-wheel effective steering angleδ′f_act can be calculated approximately by the following expression(72a). The processing in the above-described processing section 232-2-1is the process of approximately calculating δ′f_act by the expression(72a).

δ′f_act=cos(θcf)*δf_act  (72a)

To further improve the accuracy of δ′f_act, δ′f_act may be obtained by amapping from δf_act. Alternatively, to still further improve theaccuracy of δ′f_act, δ′f_act may be obtained by a mapping(two-dimensional mapping) or the like from δf_act and a detected rollangle φb_act.

The processing section 232-2 further calculates a sine valuesin(δ′f_act) of the above-described estimated front-wheel effectivesteering angle δ′f_act and multiplies the estimated front-wheelrotational transfer velocity Vf_act at the current time by the sinevalue, in a processing section 232-2-2 and a processing section 232-2-3,to thereby calculate a transfer velocity in the Y-axis direction (inother words, a component in the Y-axis direction of Vf_act) of theground contact part of the front wheel 203 f.

Further, the processing section 232-2 multiplies, in a processingsection 232-2-4, the value as a result of calculation in the processingsection 232-2-3 by Lr/L (where L=Lf+Lr), to thereby obtain a secondestimated lateral velocity component Vby_act_(—)2(=Vf_act*sin(δ′f_act)*(Lr/L)).

It should be noted that the above-described Lr and Lf in this processinghave the same meanings as those in the two-wheeled vehicle 201 in FIG.11. That is, Lr refers to a distance in the X-axis direction between theground contact point of the rear wheel 203 r and the overall center ofgravity G in the basic posture state of the two-wheeled vehicle 201A,and Lf refers to a distance in the X-axis direction between the groundcontact point of the rear wheel 203 f and the overall center of gravityG in the basic posture state of the two-wheeled vehicle 201A.

The values of Lr and Lf and the caster angle θcf have been preset forthe two-wheeled vehicle 201A, and are stored in a memory in the controldevice 215.

Further, the processing section 232-3 multiplies, in a processingsection 232-3-1, a detected rear-wheel steering angle δr_act at thecurrent time by a cosine value cos(θcr) of the caster angle θcr of therear wheel 203 r, to thereby calculate an estimate of the actual valueδ′r_act (hereinafter, referred to as “estimated rear-wheel effectivesteering angle δ′r_act”) of a rear-wheel effective steering angle δ′rwhich corresponds to the rotational angle in the yaw direction of therear wheel 203 r.

Supplementally, the rear-wheel effective steering angle δ′r is an angleof the line of intersection of the ground surface 110 and the rotationalplane of the rear wheel 203 r being steered (plane passing through thecenter of the axle of the rear wheel 203 r and orthogonal to the axlecenterline Cr thereof) with respect to the longitudinal direction(X-axis direction) of the vehicle body 202.

In the case where the roll angle φb of the vehicle body 202 isrelatively small, the estimated rear-wheel effective steering angleδ′r_act can be calculated approximately by the following expression(72b). The processing in the above-described processing section 232-3-1is the process of approximately calculating δ′r_act by the expression(72b).

δ′r_act=cos(θcr)*δr_act  (72b)

To further improve the accuracy of δ′r_act, δ′_act may be obtained by amapping from δr_act. Alternatively, to still further improve theaccuracy of δ′r_act, δ′r_act may be obtained by a mapping(two-dimensional mapping) or the like from δr_act and a detected rollangle φb_act.

The processing section 232-3 further calculates a sine valuesin(δ′r_act) of the above-described estimated rear-wheel effectivesteering angle δ′r_act and multiplies the estimated rear-wheelrotational transfer velocity Vr_act at the current time by the sinevalue, in a processing section 232-3-2 and a processing section 232-3-3,to thereby calculate a transfer velocity in the Y-axis direction (inother words, a component in the Y-axis direction of Vr_act) of theground contact part of the rear wheel 203 r.

Further, the processing section 232-3 multiplies, in a processingsection 232-3-4, the value as a result of calculation in the processingsection 232-3-3 by Lf/L (where L=Lf+Lr), to thereby obtain a thirdestimated lateral velocity component Vby_act_(—)3(=Vr_act*sin(δ′r_act)*(Lf/L)).

The value of the caster angle θcr used in the processing in theprocessing section 232-3 has also been preset for the two-wheeledvehicle 201A, as with the values of Lf, Lr, and θcf, and is stored inthe memory in the control device 215.

The estimated inverted pendulum mass point lateral velocity calculatingsection 232 sums up, in the processing section 232-4, the firstestimated lateral velocity component Vby_act_(—)1, the second estimatedlateral velocity component Vby_act_(—)2, and the third estimated lateralvelocity component Vby_act_(—)3 calculated in the above-describedmanner, to calculate an estimated inverted pendulum mass point lateralvelocity Vby_act.

Accordingly, the estimated inverted pendulum mass point lateral velocityVby_act is calculated by the following expression (73).

$\begin{matrix}\begin{matrix}{{Vby\_ act} = {{{Vby\_ act}\_ 1} + {{Vby\_ act}\_ 2} + {{Vby\_ act}\_ 3}}} \\{= {{{Pb\_ diff}{\_ y}{\_ dot}{\_ act}} + {{Vf\_ act}*{\sin \left( {\delta^{\prime}{f\_ act}} \right)}*}}} \\{{\left( {{Lr}/L} \right) + {{Vr\_ act}*{\sin \left( {\delta^{\prime}{r\_ act}} \right)}*\left( {{Lf}/L} \right)}}} \\{= {{{Pb\_ diff}{\_ y}{\_ dot}{\_ act}} + {{Vf\_ act}*{\sin \left( {{\delta f\_ act}*{\cos \left( {\theta \; {cf}} \right)}} \right)}}}} \\{{{*\left( {{Lr}/L} \right)} + {{Vr\_ act}*{\sin \left( {{\delta r\_ act}*{\cos \left( {\theta \; {cr}} \right)}} \right)}*\left( {{Lf}/L} \right)}}}\end{matrix} & (73)\end{matrix}$

It should be noted that in the case where the magnitudes of the value ofthe aforesaid conversion function Plfy(δf) corresponding to the actualsteering angle δf_act of the front wheel 203 f and the value of theaforesaid conversion function Plry(δr) corresponding to the actualsteering angle δr_act of the front wheel 203 r are sufficiently small(when the magnitudes of δf_act and δr_act are small), a differentialvalue of the value of Pb_diff_y_act obtained by ignoring the second termand the third term on the right side of the expression (71) may beadopted as Pb_diff_y_dot_act for use in the expression (73). That is, inthe expression (73), a value, multiplied by −h′, of the differentialvalue of the detected roll angle φb_act of the vehicle body 202, or avalue, multiplied by −h′, of the detected value of the roll angularvelocity (temporal change rate of the roll angle) of the vehicle body202, may be used instead of Pb_diff_y_dot_act. With this configuration,the computational load of the control device 215 can be reduced.

Next, the control device 215 carries out the processing in the estimatedtraveling speed calculating section 233.

As shown in FIG. 35, the estimated traveling speed calculating section233 receives the aforesaid estimated rear-wheel rotational transfervelocity Vr_act and the aforesaid detected rear-wheel steering angleδr_act.

The estimated traveling speed calculating section 233 carries out theprocessing shown in the block diagram in FIG. 38 to calculate anestimated traveling speed Vox_act.

In FIG. 38, a processing section 233-1 represents a processing sectionwhich multiplies a detected rear-wheel steering angle δr_act at thecurrent time by a cosine value of the caster angle θcr of the rear wheel203 r (as in the aforesaid expression (72b)) to obtain the estimatedrear-wheel effective steering angle δ′r_act, which has been describedabove in conjunction with the processing section 232-2 in the estimatedinverted pendulum mass point lateral velocity calculating section 232, aprocessing section 233-2 represents a processing section which obtains acosine value cos(δ′r_act) of the estimated rear-wheel effective steeringangle δ′r_act, and a processing section 233-3 represents a processingsection which multiplies an estimated rear-wheel rotational transfervelocity Vr_act at the current time by the above-described cosine valuecos(δ′r_act) to thereby calculate an estimated traveling speed Vox_act.

Accordingly, the estimated traveling speed calculating section 233 isconfigured to calculate Vox_act by multiplying Vr_act by the cosinevalue cos(δ′r_act) of δ′r_act. That is, Vox_act is calculated by thefollowing expression (74b).

$\begin{matrix}\begin{matrix}{{Vox\_ act} = {{Vr\_ act}*{\cos \left( {\delta^{\prime}{r\_ act}} \right)}}} \\{= {{Vr\_ act}*{\cos \left( {{\delta r\_ act}*{\cos \left( {\theta \; {cr}} \right)}} \right)}}}\end{matrix} & \left( {74b} \right)\end{matrix}$

The estimated traveling speed Vox_act calculated in this mannercorresponds to a component in the X-axis direction of the estimatedrear-wheel rotational transfer velocity Vr_act.

It should be noted that the estimated traveling speed Vox_act may becalculated by multiplying the estimated front-wheel rotational transfervelocity Vf_act by a cosine value cos(δ′f_act) of the estimatedfront-wheel effective steering angle δ′f_act calculated by the aforesaidexpression (72a). That is, Vox_act may be calculated by the followingexpression (74a).

$\begin{matrix}\begin{matrix}{{Vox\_ act} = {{Vf\_ act}*{\cos \left( {\delta^{\prime}{f\_ act}} \right)}}} \\{= {{Vf\_ act}*{\cos \left( {{\delta f\_ act}*{\cos \left( {\theta \; {cf}} \right)}} \right)}}}\end{matrix} & \left( {74a} \right)\end{matrix}$

Further, in the processing of calculating Vox_act, for the estimatedrear-wheel effective steering angle δ′r_act (or the estimatedfront-wheel effective steering angle δ′f_act), the value calculated bythe estimated inverted pendulum mass point lateral velocity calculatingsection 232 as it is may be used. In this case, it is unnecessary tosupply the detected rear-wheel steering angle δr_act (or the estimatedfront-wheel effective steering angle δ′f_act) to the estimated travelingspeed calculating section 233, and the processing section 233-1 is alsounnecessary

Further, instead of the detected rear-wheel steering angle δr_act andthe estimated rear-wheel rotational transfer velocity Vr_act at thecurrent time, a value (last time's value) δr_cmd_p of the desiredrear-wheel steering angle δr_cmd, calculated by the posture controlarithmetic section 237 (described later) in the last time's controlprocessing cycle, and a value (last time's value) Vr_cmd_p of thedesired rear-wheel rotational transfer velocity Vr_cmd, calculated bythe desired rear-wheel rotational transfer velocity determining section236 (described later) in the last time's control processing cycle,respectively, may be used. More specifically, δr_cmd_p and Vr_cmd_p maybe used to perform computation similar to that in the right side of theabove expression (74b), and the resultant value(=Vr_cmd_p*cos(δr_cmd_p*cos(θcr))) may be obtained as a pseudo estimate(alternative observed value) as an alternative to the estimatedtraveling speed Vox_act.

Further, in obtaining the pseudo estimate (alternative observed value)as an alternative to the estimated traveling speed Vox_act, δr_cmd_p maybe used instead of the detected rear-wheel steering angle δr_act at thecurrent time, and the estimated rear-wheel rotational transfer velocityVr_act may be used as it is. Conversely, Vr_cmd_p may be used instead ofthe estimated rear-wheel rotational transfer velocity Vr_act at thecurrent time, and the detected rear-wheel steering angle δr_act may beused as it is.

Next, the control device 215 carries out the processing in the desiredrear-wheel rotational transfer velocity determining section 236.

As shown in FIG. 35, the desired rear-wheel rotational transfer velocitydetermining section 236 receives a detected value of the actual value ofthe accelerator manipulated variable, which is indicated by an outputfrom the aforesaid accelerator manipulation detector 221.

The desired rear-wheel rotational transfer velocity determining section236 determines a desired rear-wheel rotational transfer velocity Vr_cmdby the processing shown in the block diagram in FIG. 42, i.e. theprocessing in a processing section 236-1.

The processing section 236-1 determines the desired rear-wheelrotational transfer velocity Vr_cmd from a detected value of theaccelerator manipulated variable at the current time, by a presetconversion function.

The conversion function is a function which is defined, for example, bya mapping or an arithmetic expression. This conversion function isbasically set such that Vr_cmd determined by the conversion functionincreases monotonically as the accelerator manipulated variableincreases.

The conversion function is set, for example, with the trend asillustrated by the graph in FIG. 42. In this case, the processingsection 236-1 determines Vr_cmd to be zero when the detected value ofthe accelerator manipulated variable falls within the dead band range(range near zero) from zero to a prescribed first acceleratormanipulated variable A1.

Further, when the detected value of the accelerator manipulated variablefalls within the range from the first accelerator manipulated variableA1 to a prescribed second accelerator manipulated variable A2 (>A1), theprocessing section 236-1 determines Vr_cmd such that Vr_cmd increasesmonotonically as the accelerator manipulated variable increases and thatthe rate of increase of Vr_cmd (increase of Vr_cmd per unit increase ofthe accelerator manipulated variable) increases smoothly.

When the detected value of the accelerator manipulated variable fallswithin the range from the second accelerator manipulated variable A2 toa prescribed third accelerator manipulated variable A3 (>A2), theprocessing section 236-1 determines Vr_cmd such that Vr_cmd increasesmonotonically, at a constant rate of increase, as the acceleratormanipulated variable increases.

Further, when the detected value of the accelerator manipulated variableexceeds the third accelerator manipulated variable A3, the processingsection 236-1 determines Vr_cmd such that it remains at a constant value(at the value corresponding to A3).

Next, the control device 215 carries out the processing in the controlgain determining section 235. As shown in FIG. 35, the control gaindetermining section 235 receives, via a delay element 238, a last time'sdesired rear-wheel steering angle δr_cmd_p, which is a value (lasttime's value) of the desired rear-wheel steering angle δr_cmd determinedby the posture control arithmetic section 237 in the last time's controlprocessing cycle of the control device 215. The control gain determiningsection 235 also receives an estimated traveling speed Vox_actcalculated by the estimated traveling speed calculating section 233 inthe current time's control processing cycle.

The control gain determining section 235 carries out the processingshown in the block diagram in FIG. 39, for example, to determine valuesof a plurality of gains K1, K2, K3, and K4 for the posture control ofthe vehicle body 202.

The values of the gains K1, K2, K3, and K4 are each determined variablyin accordance with δr_cmd_p and Vox_act, or in accordance with Vox_act,as will be described in detail later.

Next, the control device 215 carries out the processing in the desiredposture state determining section 234. The desired posture statedetermining section 234 determines a desired inverted pendulum masspoint lateral movement amount Pb_diff_y_cmd, which is a desired value ofthe inverted pendulum mass point lateral movement amount Pb_diff_y, anda desired inverted pendulum mass point lateral velocity Vby_cmd, whichis a desired value of the inverted pendulum mass point lateral velocityVby. In the present embodiment, the desired posture state determiningsection 234 sets both of Pb_diff_y_cmd and Vby_cmd to zero, by way ofexample.

Next, the control device 215 carries out the processing in the posturecontrol arithmetic section 237. As shown in FIG. 35, the posture controlarithmetic section 237 receives the desired inverted pendulum mass pointlateral movement amount Pb_diff_y_cmd and the desired inverted pendulummass point lateral velocity Vby_cmd determined in the desired posturestate determining section 234, the estimated inverted pendulum masspoint lateral movement amount Pb_diff_y_act calculated in the estimatedinverted pendulum mass point lateral movement amount calculating section231, the estimated inverted pendulum mass point lateral velocity Vby_actcalculated in the estimated inverted pendulum mass point lateralvelocity calculating section 232, and the gains K1, K2, K3, and K4determined in the control gain determining section 235.

The posture control arithmetic section 237 uses the above-describedinput values to carry out the processing shown in the block diagram inFIG. 43, to thereby determine a desired rear-wheel steering angleδr_cmd, a desired rear-wheel steering angular velocity δr_dot_cmd, and adesired rear-wheel steering angular acceleration δr_dot2_cmd.

In FIG. 43, a processing section 237-1 represents a processing sectionwhich obtains a deviation of Pb_diff_y_act from Pb_diff_y_cmd, aprocessing section 237-2 represents a processing section whichmultiplies the output of the processing section 237-1 by the gain K1, aprocessing section 237-3 represents a processing section which obtains adeviation of Vby_act from Vby_cmd, a processing section 237-4 representsa processing section which multiplies the output of the processingsection 237-3 by the gain K2, a processing section 237-5 represents aprocessing section which multiplies δr_cmd_p by the gain K3, aprocessing section 237-6 represents a processing section whichmultiplies a last time's desired rear-wheel steering angular velocityδr_dot_cmd_p, which is a value of the desired rear-wheel steeringangular velocity δr_dot_cmd determined by the posture control arithmeticsection 237 in the last time's control processing cycle, by the gain K4,and a processing section 237-7 represents a processing section whichsums up the outputs from the processing sections 237-2 and 237-4 and thevalues, each multiplied by −1, of the outputs from the processingsections 237-5 and 237-6, to thereby calculate a desired rear-wheelsteering angular acceleration δr_dot2_cmd.

Further, a processing section 237-8 represents a processing sectionwhich integrates the output of the processing section 237-7 to obtain adesired rear-wheel steering angular velocity δr_dot_cmd, a processingsection 237-9 represents a delay element which outputs the output fromthe processing section 237-8 in the last time's control processing cycle(i.e. last time's desired rear-wheel steering angular velocityδr_dot_cmd_p) to the processing section 237-6, a processing section237-10 represents a processing section which integrates the output ofthe processing section 237-8 to obtain a desired rear-wheel steeringangle δr_cmd, and a processing section 237-11 represents a delay elementwhich outputs the output from the processing section 237-10 in the lasttime's control processing cycle (i.e. last time's desired rear-wheelsteering angle δr_cmd_p) to the processing section 237-5.

Accordingly, the posture control arithmetic section 237 calculates thedesired rear-wheel steering angular acceleration δr_dot2_cmd by thefollowing expression (75).

$\begin{matrix}{{{\delta r\_ dot2}{\_ cmd}} = {{K\; 1*\left( {{{Pb\_ diff}{\_ y}{\_ cmd}} - {{Pb\_ diff}{\_ y}{\_ act}}} \right)} + {K\; 2*\left( {{Vby\_ cmd} - {Vby\_ act}} \right)} - {K\; 3*{\delta r\_ cmd}{\_ p}} - {K\; 4*{\delta r\_ dot}{\_ cmd}{\_ p}}}} & (75)\end{matrix}$

In the above expression (75), K1*(Pb_diff_y_cmd−Pb_diff_y_act) is afeedback manipulated variable having the function of making thedeviation (Pb_diff_y_cmd−Pb_diff_y_act) approach “0”,K2*(Vby_cmd−Vby_act) is a feedback manipulated variable having thefunction of making the deviation (Vby_cmd−Vby_act) approach “0”,−K3*δr_cmd_p is a feedback manipulated variable having the function ofmaking δr_cmd approach “0”, and −K4*δr_dot_cmd_p is a feedbackmanipulated variable having the function of making δr_dot_cmd approach“0”.

The posture control arithmetic section 237 integrates δr_dot2_cmddetermined by the above expression (75) to determine a desiredrear-wheel steering angular velocity δr_dot_cmd. Further, the posturecontrol arithmetic section 237 integrates this δr_dot_cmd to determine adesired rear-wheel steering angle δr_cmd.

It should be noted that δr_cmd_p and δr_dot_cmd_p used in thecomputation of the expression (75) have the meanings as pseudo estimates(alternative observed values) of the actual steering angle and steeringangular velocity, respectively, of the rear wheel 203 r at the currenttime. Therefore, instead of θr_cmd_p, a detected rear-wheel steeringangle δr_act at the current time may be used. Further, instead ofδr_dot_cmd_p, a detected rear-wheel steering angular velocity δr_dot_act(detected value of the actual steering angular velocity of the rearwheel 203 r) based on an output from the aforesaid rear-wheel steeringangle detector 218 may be used.

The above has described the processing in the posture control arithmeticsection 237.

In accordance with the processing in the posture control arithmeticsection 237, the desired rear-wheel steering angular accelerationδr_dot2_cmd is basically determined such that any divergence of theactual inverted pendulum mass point lateral movement amount (estimatedinverted pendulum mass point lateral movement amount Pb_diff_y_act) ofthe two-wheeled vehicle 201A from the desired inverted pendulum masspoint lateral movement amount Pb_diff_y_cmd, or any divergence of theactual inverted pendulum mass point lateral velocity (estimated invertedpendulum mass point lateral velocity Vby_act) of the two-wheeled vehicle201A from the desired inverted pendulum mass point lateral velocityVby_cmd, is eliminated through manipulation of the steering angle δr ofthe rear wheel 203 r (and, hence, that the actual inverted pendulum masspoint lateral movement amount or lateral velocity of the two-wheeledvehicle 201A is restored to the desired inverted pendulum mass pointlateral movement amount Pb_diff_y_cmd or desired inverted pendulum masspoint lateral velocity Vby_cmd).

Further, in the present embodiment, the desired inverted pendulum masspoint lateral movement amount Pb_diff_y_cmd is “0”. Therefore, in thestate where the actual inverted pendulum mass point lateral movementamount of the two-wheeled vehicle 201A is held at a value whichcoincides, or almost coincides, with the desired inverted pendulum masspoint lateral movement amount Pb_diff_y_cmd, the desired rear-wheelsteering angular acceleration δr_dot2_cmd is determined so as to keepthe actual steering angle of the rear wheel 203 r at “0” or almost “0”.

Here, the gains K1 to K4 (feedback gains related to the respectivefeedback manipulated variables in the right side of the aforesaidexpression (75)) used for calculating δr_dot2_cmd by the computation ofthe expression (75) are determined in the aforesaid control gaindetermining section 235. The processing in the control gain determiningsection 235 will now be described in detail.

The control gain determining section 235 determines the values of thegains K1 to K4 from the received estimated traveling speed Vox_act andlast time's desired rear-wheel steering angle δr_cmd_p, by theprocessing shown in the block diagram in FIG. 39.

In FIG. 39, a processing section 235-1 is a processing section whichdetermines the gain K1 in accordance with Vox_act and δr_cmd_p, and aprocessing section 235-2 is a processing section which determines thegain K2 in accordance with Vox_act and δr_cmd_p.

In the present embodiment, the processing section 235-1 determines thegain K1 from Vox_act and δr_cmd_p, in accordance with a presettwo-dimensional mapping (conversion function of two variables).Similarly, the processing section 235-2 determines the gain K2 fromVox_act and δr_cmd_p, in accordance with a preset two-dimensionalmapping (conversion function of two variables).

In these two-dimensional mappings, the trend of the change in value ofthe gain K1 with respect to Vox_act and δr_cmd_p and the trend of thechange in value of the gain K2 with respect to Vox_act and δr_cmd_p areset substantially similar to each other.

Specifically, as illustrated by the graphs shown in the processingsections 235-1 and 235-2 in FIG. 39, the two-dimensional mappings in theprocessing sections 235-1 and 235-2 are each set such that the magnitudeof the gain K1, K2 determined by the two-dimensional mapping has thetrend of monotonically decreasing with increasing Vox_act when δr_cmd_pis fixed to a given value.

Accordingly, the gains K1 and K2 as the feedback gains related to thefeedback manipulated variables having the function of stabilizing theposture in the roll direction of the vehicle body 202 of the two-wheeledvehicle 201A (making the estimated inverted pendulum mass point lateralmovement amount Pb_diff_y_act and the estimated inverted pendulum masspoint lateral velocity Vby_act converge respectively to Pb_diff_y_cmdand Vby_cmd) are determined such that the magnitudes of the gains K1 andK2 each become smaller as the actual traveling speed (estimatedtraveling speed Vox_act) of the two-wheeled vehicle 201A becomesgreater.

In other words, the gains K1 and K2 are determined such that the controlfunction for stabilizing the posture in the roll direction of thevehicle body 202 by performing the steering control of the rear wheel203 r so as to make Pb_diff_y_act and Vby_act converge to Pb_diff_y_cmdand Vby_cmd, respectively, is reduced when the actual traveling speed(estimated traveling speed Vox_act) of the two-wheeled vehicle 201A isin a high-speed range, as compared to when it is in a low-speed range.

Accordingly, in the case where the actual traveling speed (estimatedtraveling speed Vox_act) of the two-wheeled vehicle 201A is relativelyhigh, i.e. in the state where the posture in the roll direction of thevehicle body 202 is unlikely to become unstable, a rider of thetwo-wheeled vehicle 201A can readily change the posture in the rolldirection (roll angle φb) of the vehicle body 202 by shifting the weightof the rider's body and so on, as in the case of a conventionaltwo-wheeled vehicle (which is not provided with the function ofcontrolling the posture in the roll direction of the vehicle body).

It should be noted that the two-dimensional mappings for determining thegains K1 and K2 may each be set such that the value of K1, K2 isdetermined to be “0” or almost “0” when the estimated traveling speedVox_act reaches a certain level of speed.

With this configuration, the function of controlling the posture in theroll direction of the vehicle body 202 becomes substantially OFF whenthe actual traveling speed (estimated traveling speed Vox_act) of thetwo-wheeled vehicle 201A is relatively high. This can make thebehavioral characteristics of the two-wheeled vehicle 201A approach thecharacteristics comparable to those of a conventional two-wheeledvehicle in the case where the actual traveling speed of the two-wheeledvehicle 201A is high.

Further, the two-dimensional mappings in the processing sections 235-1and 235-2 are each set such that the gain K1, K2 determined by themapping has the trend of monotonically decreasing with increasingmagnitude (absolute value) of δr_cmd_p when Vox_act is fixed to a givenvalue.

Accordingly, the gains K1 and K2 as the gains related to the feedbackmanipulated variables having the function of stabilizing the posture inthe roll direction of the vehicle body 202 of the two-wheeled vehicle201A are determined such that the magnitudes of the gains K1 and K2 eachbecome smaller as the magnitude of δr_cmd_p, corresponding to the actualsteering angle of the rear wheel 203 r, becomes larger.

The magnitudes of the gains K1 and K2 are changed as described above,for the following reason. In the case where the magnitude of the actualsteering angle of the rear wheel 203 r is large, compared to the casewhere it is small, the radius of curvature of the ground contact part ofthe steering control wheel (rear wheel 203 r) as seen in a cross sectionincluding the ground contact point of the steering control wheel (rearwheel 203 r) and having a normal in the X-axis direction (longitudinaldirection of the vehicle body 202) becomes larger, as explained above.

Therefore, in the case where the magnitude of the actual steering angleof the rear wheel 203 r is large, compared to the case where it issmall, the change in movement amount of the ground contact point of therear wheel 203 r according to the change in the steering becomes larger.Because of this, if the magnitudes of the gains K1 and K2 are setindependently of the actual steering angle, oscillation is likely tooccur in the control of the posture in the roll direction of the vehiclebody 202 of the two-wheeled vehicle 201A.

When it is configured such that the magnitudes of the gains K1 and K2are changed in accordance with the magnitude of δr_cmd_p, as describedabove, the above-described oscillation can be prevented even in the casewhere the magnitude (absolute value) of the actual steering angle of therear wheel 203 r is large.

In the block diagram in FIG. 39, processing sections 235-3 and 235-4represent processing sections which determine the gains K3 and K4,respectively, in accordance with Vox_act.

In the present embodiment, the processing sections 235-3 and 235-4determine the gains K3 and K4, respectively, from Vox_act, in accordancewith conversion functions defined by preset mappings (or arithmeticexpressions).

These conversion functions are set, as illustrated by the graphs shownin the processing sections 235-3 and 235-4 in FIG. 39, such thatbasically the gains K3 and K4 each increase monotonically, between aprescribed upper limit and a prescribed lower limit, as Vox_actincreases.

In this case, in the conversion functions in the processing sections235-3 and 235-4, in the region where Vox_act takes a value near “0”, K3and K4 are each maintained at the lower limit. In the region whereVox_act takes a sufficiently large value, K3 and K4 are each maintainedat the upper limit.

As the gains K3 and K4 are determined in the above-described manner, thegains K3 and K4 as the feedback gains related to the feedbackmanipulated variables having the function of making the steering angleδr of the rear wheel 203 r approach zero are determined such that themagnitudes of the gains K3 and K4 become relatively large in the casewhere the actual traveling speed (estimated traveling speed Vox_act) ofthe two-wheeled vehicle 201A is relatively high (in a high-speed range),compared to the case where the actual traveling speed of the two-wheeledvehicle 201A is relatively low (in a low-speed range (including “0”)).

Here, in an ordinary two-wheeled vehicle, when it is traveling at arelatively high speed, the steering control wheel is usually held in anon-steered state or nearly non-steered state. Therefore, setting thegains K3 and K4 in the above-described manner can allow the steeringcharacteristics of the rear wheel 203 r of the two-wheeled vehicle 201Awhen the actual traveling speed of the two-wheeled vehicle 201A isrelatively high to approach the characteristics of the ordinarytwo-wheeled vehicle.

The above has described the details of the processing in the controlgain determining section 235 according to the present embodiment.

In the processing in the aforesaid processing sections 235-1 and 235-2,the gains K1 and K2 were determined in accordance with Vox_act andδr_cmd_p by using two-dimensional mappings. The gains K1 and K2,however, may be determined in another manner not using thetwo-dimensional mappings.

For example, the gains K1 and K2 may be determined by the processing inprocessing sections 235-6 and 235-7 in the block diagram in FIG. 40 or41. It should be noted that, except for the processing in the processingsections 235-6 and 235-7, the processing in the block diagram in each ofFIGS. 40 and 41 is identical to the processing in the block diagram inFIG. 39.

The processing section 235-6 in FIG. 40 includes a processing section235-6-1 which determines a first adjustment parameter Kv_(—)1 foradjusting the value of the gain K1, from Vox_act, by a preset conversionfunction, a processing section 235-6-2 which determines a secondadjustment parameter Kδ_(—)1 for adjusting the value of the gain K1,from δr_cmd_p, by a preset conversion function, a processing section235-6-3 which determines a composite adjustment parameter(=Kv_(—)1*Kδ_(—)1) by multiplying the adjustment parameters Kv_(—)1 andKδ_(—)1, and a processing section 235-6-4 which adds this compositeadjustment parameter to a prescribed reference value (lower limit)K0_(—)1 of the gain K1, to thereby determine the gain K1(=Kv_(—)1*Kδ_(—)1+K0_(—)1).

The processing section 235-7 includes a processing section 235-7-1 whichdetermines a first adjustment parameter Kv_(—)2 for adjusting the valueof the gain K2, from Vox_act, by a preset conversion function, aprocessing section 235-7-2 which determines a second adjustmentparameter Kδ_(—)2 for adjusting the value of the gain K2, from δr_cmd_p,by a preset conversion function, a processing section 235-7-3 whichdetermines a composite adjustment parameter (=Kv_(—)2*Kδ_(—)2) bymultiplying the adjustment parameters Kv_(—)2 and Kδ_(—)2, and aprocessing section 235-7-4 which adds this composite adjustmentparameter to a prescribed reference value (lower limit) K0_(—)2 of thegain K2, to thereby determine the gain K2 (=Kv_(—)2*Kδ_(—)2+K0_(—)2).

In this case, the conversion functions of the respective processingsections 235-6-1, 235-7-1, 235-6-2, and 235-7-2 are each defined, forexample, by a mapping (one-dimensional mapping) or an arithmeticexpression.

The conversion functions of the processing sections 235-6-1 and 235-7-1are set, as illustrated by the graphs shown in the processing sections235-6-1 and 235-7-1 in FIG. 40, such that Kv_(—)1 and Kv_(—)2 determinedby the respective conversion functions each decrease monotonically (toapproach zero) from a prescribed upper limit (>0) as Vox_act becomeslarger.

Accordingly, in a low-speed range where Vox_act is relative small,Kv_(—)1 and Kv_(—)2 are each set to an effective positive value (havinga magnitude above a certain level).

Further, the conversion functions of the processing sections 235-6-2 and235-7-2 are set, as illustrated by the graphs shown in the processingsections 235-6-2 and 235-7-2 in FIG. 40, such that Kδ_(—)1 and Kδ_(—)2determined by the respective conversion functions each decreasemonotonically as the magnitude (absolute value) of δr_cmd_p increases.

More specifically, Kδ_(—)1 and Kδ_(—)2 are determined such that theyeach attain a prescribed upper limit (>0) when the magnitude of δr_cmd_pis “0”, and that Kδ_(—)1 and Kδ_(—)2 each decrease down to a prescribedlower limit (>0) as the magnitude of δr_cmd_p increases from “0”.

Therefore, the processing sections 235-6 and 235-7 shown in FIG. 40 candetermine the gains K1 and K2, respectively, such that the trends of thechanges of K1 and K2 with respect to Vox_act and δr_cmd_p become similarto the trends of the changes of K1 and K2 determined by the processingsections 235-1 and 235-2, respectively, in FIG. 39.

The processing sections 235-6 and 235-7 in FIG. 41 are different fromthose in FIG. 40 only in part of the processing.

Specifically, the processing section 235-6 in FIG. 41 adopts aprocessing section 235-6-5 as a processing section for determining thefirst adjustment parameter Kv_(—)1 for adjusting the value of the gainK1 in accordance with Vox_act, instead of the processing section 235-6-1shown in FIG. 40. Except for the processing section 235-6-5, theconfiguration of the processing section 235-6 in FIG. 41 is identical tothat in FIG. 40.

Similarly, the processing section 235-7 in FIG. 41 adopts a processingsection 235-7-5, instead of the processing section 235-7-1 shown in FIG.40, as a processing section for determining the first adjustmentparameter Kv_(—)2 for adjusting the value of the gain K2 in accordancewith Vox_act. Except for the processing section 235-7-5, theconfiguration of the processing section 235-7 in FIG. 41 is identical tothat in FIG. 40.

The processing sections 235-6-5 and 235-7-5 use conversion functions(mappings or arithmetic expressions) for determining Kv_(—)1 andKv_(—)2, respectively, which are different from those used in FIG. 40.

Specifically, the conversion functions in the processing sections235-6-5 and 235-7-5 are set, as illustrated by the graphs shown in theprocessing sections 235-6-5 and 235-7-5 in FIG. 41, such that Kv_(—)1and Kv_(—)2 determined by the respective conversion functions eachmonotonically decrease with increasing Vox_act and, additionally, suchthat Kv_(—)1 and Kv_(—)2 are each set to zero (or almost zero) in ahigh-speed range where Vox_act becomes high.

It should be noted that the reference value (lower limit) K0_(—)1 of thegain K1 in the processing section 235-6 in FIG. 41 and the referencevalue (lower limit) K0_(—)2 of the gain K2 in the processing section235-7 in FIG. 41 are each set to zero or a value near zero.

Therefore, the processing sections 235-6 and 235-7 shown in FIG. 41 candetermine the gains K1 and K2, respectively, such that the trends of thechanges of K1 and K2 with respect to Vox_act and δr_cmd_p become similarto the trends of the changes of K1 and K2 determined by the processingsections 235-1 and 235-2, respectively, in FIG. 39.

In addition, in a high-speed range where the actual traveling speed ofthe two-wheeled vehicle 201A is high, both of the gains K1 and K2 areset to zero or almost zero. This can make the behavioral characteristicsof the two-wheeled vehicle 201A still further approach thecharacteristics comparable to those of a conventional two-wheeledvehicle in the case where the actual traveling speed of the two-wheeledvehicle 201A is high.

It should be noted that for the conversion functions for determining thegains K1 and K2, conversion functions in other forms may be adopted, aslong as they can determine the gains with the above-described trendswith respect to Vox_act and δr_cmd_p. Similarly, for the conversionfunctions for determining the gains K3 and K4, conversion functions inother forms may be adopted, as long as they can determine the gains withthe above-described trends with respect to Vox_act.

Supplementally, the last time's desired rear-wheel steering angleδr_cmd_p has the meaning as a pseudo estimate (alternative observedvalue) of the actual steering angle of the rear wheel 203 r at thecurrent time.

Accordingly, for determining the respective gains K1, K2, K3, and K4,the aforesaid detected rear-wheel steering angle δr_act may be usedinstead of δr_cmd_p.

Further, in the case where the response of the rear-wheel drivingactuator 209 is sufficiently quick, the value of the traveling speed(=Vr_cmd_p*cos(δr_cmd_p*cos(θcr)), hereinafter referred to as “lasttime's desired traveling speed Vox_cmd_p”) calculated by the computationsimilar to that in the aforesaid expression (74b) from theabove-described last time's desired rear-wheel steering angle δr_cmd_pand a last time's desired rear-wheel rotational transfer velocityVr_cmd_p (desired rear-wheel rotational transfer velocity Vr_cmddetermined by the desired rear-wheel rotational transfer velocitydetermining section 236 in the last time's control processing cycle) hasthe meaning as a pseudo estimate (alternative observed value) of theactual traveling speed of the two-wheeled vehicle 201A at the currenttime.

Accordingly, for determining the respective gains K1, K2, K3, and K4,the above-described last time's desired traveling speed Vox_cmd_p may beused instead of Vox_act.

Controls of the aforesaid rear-wheel steering actuator 208 andrear-wheel driving actuator 209 will now be described.

The control device 215 further includes, as functions other than thefunctions shown in FIG. 35, a rear-wheel steering actuator controlsection 241 shown in FIG. 44 and a rear-wheel driving actuator controlsection 242 shown in FIG. 45.

The rear-wheel steering actuator control section 241 carries out drivecontrol of the rear-wheel steering actuator 208, by the controlprocessing shown in the block diagram in FIG. 44, for example, to causethe actual steering angle (detected rear-wheel steering angle δr_act) ofthe rear wheel 203 r to track a desired rear-wheel steering angleδr_cmd.

In this example, the rear-wheel steering actuator control section 241receives a desired rear-wheel steering angle δr_cmd, a desiredrear-wheel steering angular velocity δr_dot_cmd, and a desiredrear-wheel steering angular acceleration δr_dot2_cmd determined in theabove-described manner in the posture control arithmetic section 237, adetected rear-wheel steering angle δr_act, and a detected rear-wheelsteering angular velocity δr_dot_act which is a detected value of theactual steering angular velocity of the rear wheel 203 r.

It should be noted that the detected rear-wheel steering angularvelocity δr_dot_act is a value of the steering angular velocity which isrecognized on the basis of an output from the rear-wheel steering angledetector 218, or a value obtained by calculating a temporal change rateof the detected rear-wheel steering angle δr_act.

The rear-wheel steering actuator control section 241 performs theprocessing in an electric current command value determining section241-1 to determine, from the above-described input values, an electriccurrent command value I_δr_cmd which is a desired value of the electriccurrent passed through the rear-wheel steering actuator 208 (electricmotor).

The electric current command value determining section 241-1 determinesthe electric current command value I_δr_cmd by summing up a feedbackmanipulated variable component obtained by multiplying a deviation ofδr_act from δr_cmd by a gain Kδr_p of a prescribed value, a feedbackmanipulated variable component obtained by multiplying a deviation ofδr_dot_act from δr_dot_cmd by a gain Kδr_v of a prescribed value, and afeedforward manipulated variable component obtained by multiplyingδr_dot2_cmd by a gain Kδr_a of a prescribed value, as shown by thefollowing expression (77).

$\begin{matrix}{{{I\_\delta r}{\_ cmd}} = {{{K\delta r\_ p}*\left( {{\delta r\_ cmd} - {\delta r\_ act}} \right)} + {{K\delta r\_ v}*\left( {{{\delta r\_ dot}{\_ cmd}} - {{\delta r\_ dot}{\_ act}}} \right)} + {{K\delta r\_ a}*{\delta r\_ dot2}{\_ cmd}}}} & (77)\end{matrix}$

The rear-wheel steering actuator control section 241 then controls theactual electric current passed through the rear-wheel steering actuator208 (electric motor) to match the electric current command valueI_δr_cmd, by an electric current control section 241-2 which is made upof a motor driver or the like.

In this manner, the control is performed such that the actual steeringangle of the rear wheel 203 r tracks the desired rear-wheel steeringangle δr_cmd. In this case, the electric current command value I_δr_cmdincludes the third term on the right side of the above expression (77),i.e. the feedforward manipulated variable component, ensuring improvedtracking in the above-described control.

It should be noted that the technique of controlling the rear-wheelsteering actuator 208 to cause the actual steering angle of the rearwheel 203 r to track the desired rear-wheel steering angle δr_cmd is notlimited to the above-described technique; other techniques may be usedas well. For example, various kinds of known servo control techniquesrelated to electric motors (feedback control techniques for causing theactual angle of rotation of the rotor of the electric motor to track adesired value) may be adopted.

The rear-wheel driving actuator control section 242 carries out drivecontrol of the rear-wheel driving actuator 209, by the controlprocessing shown in the block diagram in FIG. 45, for example, to causethe actual rotational transfer velocity of the rear wheel 203 r to tracka desired rear-wheel rotational transfer velocity Vr_cmd (or to causethe actual rotational angular velocity of the rear wheel 203 r to tracka desired rotational angular velocity corresponding to Vr_cmd).

In this example, the rear-wheel driving actuator control section 242receives a desired rear-wheel rotational transfer velocity Vr_cmddetermined in the above-described manner in the desired rear-wheelrotational transfer velocity determining section 236, and an estimatedrear-wheel rotational transfer velocity Vr_act.

The rear-wheel driving actuator control section 242 performs theprocessing in an electric current command value determining section242-1 to determine, from the above-described input values, an electriccurrent command value I_Vr_cmd which is a desired value of the electriccurrent passed through the rear-wheel driving actuator 209 (electricmotor).

The electric current command value determining section 242-1 determinesa feedback manipulated variable component obtained by multiplying adeviation of Vr_act from Vr_cmd by a gain KVr_v of a prescribed value,as the electric current command value I_Vr_cmd, as shown by thefollowing expression (78).

I _(—) Vr _(—) cmd=KVr _(—) v*(Vr _(—) cmd−Vr_act)  (78)

It should be noted that, instead of using the above expression (78),I_Vr_cmd may be determined by, for example, multiplying a deviation ofthe detected value of the actual rotational angular velocity of the rearwheel 203 r, which is indicated by an output from the rear-wheelrotational speed detector 220, from a value obtained by dividing Vr_cmdby the effective rolling radius of the rear wheel 203 r (i.e. a desiredvalue of the rotational angular velocity of the rear wheel 203 r) by again of a prescribed value.

The rear-wheel driving actuator control section 242 then controls theactual electric current passed through the rear-wheel driving actuator209 (electric motor) to match the electric current command valueI_Vr_cmd, by an electric current control section 242-2 which is made upof a motor driver or the like.

In this manner, the control is performed such that the actual rotationaltransfer velocity of the rear wheel 203 r tracks the desired rear-wheelrotational transfer velocity Vr_cmd (or such that the actual rotationalangular velocity tracks the desired value of the rotational angularvelocity corresponding to Vr_cmd).

It should be noted that the technique of controlling the rear-wheeldriving actuator 209 to cause the actual rotational transfer velocity ofthe rear wheel 203 r to track the desired rear-wheel rotational transfervelocity Vr_cmd is not limited to the above-described technique; othertechniques may be used as well. For example, various kinds of knownspeed control techniques related to electric motors (feedback controltechniques for causing the actual rotational angular velocity of therotor of the electric motor to track a desired value) may be adopted.

The above has described the details of the control processing in thecontrol device 215 according the present embodiment.

Here, the correspondence between the present embodiment and the presentinvention will be described. In the present embodiment, the rear wheel203 r corresponds to the steering control wheel in the presentinvention, and the rear-wheel steering actuator 208 (electric motor)corresponds to the steering actuator in the present invention.

Further, the inverted pendulum mass point 123 (first mass point 123) andthe second mass point 124 in the two-wheeled vehicle 201A correspondrespectively to the mass points A and B in the present invention. Thedynamic behavior of the system having the inverted pendulum mass point123 (first mass point 123) and the second mass point 124 is specificallyexpressed by the aforesaid expressions (19) to (27).

Further, the dynamics model of a mass point system having the invertedpendulum mass point 123 (first mass point 123) and the second mass point124 in the two-wheeled vehicle 201A corresponds to the dynamics model inthe present invention. The dynamics model is specifically expressed bythe aforesaid expressions (19) to (27).

Further, in the present embodiment, for stabilizing the posture of thevehicle body 202, the rear-wheel steering actuator 208 (electric motor)is controlled such that the inverted pendulum mass point lateralmovement amount and the inverted pendulum mass point lateral velocity,constituting the motional state quantity of the inverted pendulum masspoint 123, each approach (or converge to) zero, which is the desiredvalue (Pb_diff_y_cmd, Vby_cmd), and that the steering angle and thesteering angular velocity, constituting the motional state quantity ofthe steering angle of the steering control wheel (rear wheel 203 r),each approach (or converge to) zero, which is the desired value.

Specifically, in the processing in the posture control arithmeticsection 237, the desired rear-wheel steering angular accelerationδr_dot2_cmd as an operational target of the rear-wheel steering actuator208 (steering actuator) is determined, by a feedback control law, so asto cause a deviation of each of the estimated inverted pendulum masspoint lateral movement amount Pb_diff_y_act, the estimated invertedpendulum mass point lateral velocity Vby_act, the last time's desiredrear-wheel steering angle δr_cmd_p, representing a pseudo estimate ofthe steering angle δr, and the last time's desired rear-wheel steeringangular velocity δr_dot_cmd_p, representing a pseudo estimate of thesteering angular velocity δr_dot, from the corresponding desired valueto converge to zero.

Further, the driving force of the rear-wheel steering actuator 208 iscontrolled by the aforesaid rear-wheel steering actuator Control section241 such that the actual steering angle of the rear wheel 203 r tracks adesired rear-wheel steering angle δr_cmd which has been determined byperforming integration twice on the above-described δr_dot2_cmd.

In this manner, the rear-wheel steering actuator 208 is controlled so asto stabilize the motional state quantity of the inverted pendulum masspoint 123 and the motional state quantity of the steering angle of thesteering control wheel (rear wheel 203 r) and, hence, to stabilize theposture (in the roll direction) of the vehicle body 202.

In the present embodiment, the arrangement (relative to the rear wheel203 r) of the steering axis Csr of the rear wheel 203 r which is asteering control wheel is set such that, in the basic posture state ofthe two-wheeled vehicle 201A, the intersection point Er′ of the steeringaxis Csr and a virtual straight line connecting the center of the axleof the rear wheel 203 r and the ground contact point thereof is locatedbelow the ground surface 110 (that is, such that the height a′ of theintersection point Er′ from the ground surface 110 satisfies: a′<0).

Therefore, the condition that a′<a_sum′ (and, hence, the aforesaid“first condition” in the present invention) is naturally satisfied fora_sum′ defined by the aforesaid expression (28)′. Further, the conditionthat a′≦a_s′ (and, hence, the “second condition” in the presentinvention) is also naturally satisfied for a_s′ defined by the aforesaidexpression (40)′. Still further, the condition that a′≦Rr is alsonaturally satisfied for the radius of curvature Rr of the transversecross-sectional shape of the steering control wheel (rear wheel 203 r)in the basic posture state of the two-wheeled vehicle 201A.

According to the present embodiment described above, it is set suchthat, in the basic posture state of the two-wheeled vehicle 201A, theheight a′ of the intersection point Er′ of the steering axis Csr of therear wheel 203 r which is a steering control wheel and a virtualstraight line connecting the center of the axle of the rear wheel 203 rand the ground contact point thereof satisfies: a′<0 (and, hence,a′<a_aum′, a′≦a_s′), as described above. As a result, the height a′ isset to satisfy the aforesaid “first condition” and “second condition”.

Therefore, in the case where the actual inverted pendulum mass pointlateral movement amount (estimated inverted pendulum mass point lateralmovement amount Pb_diff_y_act) of the two-wheeled vehicle 201A deviatesfrom the desired inverted pendulum mass point lateral movement amountPb_diff_y_cmd (in other words, in the case where the actual posture ofthe vehicle body 202 deviates from the desired posture satisfyingPb_diff_y_act=0), the steering of the rear wheel 203 r by the drivingforce of the rear-wheel steering actuator 208 can cause a moment (in theroll direction) capable of making the actual inverted pendulum masspoint lateral movement amount of the two-wheeled vehicle 201A smoothlyrestored to the desired inverted pendulum mass point lateral movementamount Pb_diff_y_cmd to act on the vehicle body 202, without the needfor the rider to intentionally move the steering handlebar 207. That is,it is possible to cause the moment in the roll direction for stabilizingthe posture of the vehicle body 202 to act on the vehicle body 202.

According to this moment, the actual roll angle of the vehicle body 202is changed, so that the actual inverted pendulum mass point lateralmovement amount is restored to the desired inverted pendulum mass pointlateral movement amount Pb_diff_y_cmd. It should be noted that theactual inverted pendulum mass point lateral movement amount beingrestored to the desired inverted pendulum mass point lateral movementamount Pb_diff_y_cmd more specifically means that the actual roll angleof the vehicle body 202 and the actual steering angle of the rear wheel203 r are controlled so as to cause the estimated inverted pendulum masspoint lateral movement amount Pb_diff_y_act, calculated by the aforesaidexpression (71) from the actual roll angle of the vehicle body 202, theactual steering angle of the front wheel 203 f, and the actual steeringangle of the rear wheel 203 r, to match the desired inverted pendulummass point lateral movement amount Pb_diff_y_cmd.

At this time, the sensitivity of the above-described moment generated inaccordance with the change in steering angle of the rear wheel 203 r isrelatively high. Therefore, the actual inverted pendulum mass pointlateral movement amount of the two-wheeled vehicle 201A can be restoredto the desired inverted pendulum mass point lateral movement amountPb_diff_y_cmd, without causing an excessive change in steering angle ofthe rear wheel 203 r.

Further, through calculation of the desired rear-wheel steering angularacceleration δr_dot2_cmd by the aforesaid expression (75), the desiredrear-wheel steering angular acceleration δr_dot2_cmd (operational targetof the rear-wheel steering actuator 208) is determined to make adeviation (Pb_diff_y_cmd−Pb_diff_y_act) of the estimated invertedpendulum mass point lateral movement amount Pb_diff_y_act, representingan observed value of the current actual inverted pendulum mass pointlateral movement amount, from the desired inverted pendulum mass pointlateral movement amount Pb_diff_y_cmd of the two-wheeled vehicle 201A, adeviation (Vby_cmd−Vby_act) of the estimated inverted pendulum masspoint lateral velocity Vby_act, representing an observed value of thecurrent actual inverted pendulum mass point lateral velocity, from thedesired inverted pendulum mass point lateral velocity Vby_cmd of thetwo-wheeled vehicle 201A, the last time's desired rear-wheel steeringangle δr_cmd_p, representing a pseudo estimate of the current actualsteering angle (from the neutral steering angle) of the rear wheel 203r, and the last time's desired rear-wheel steering angular velocityδr_dot_cmd_p, representing a pseudo estimate of the angular velocity ofthe current actual steering angle of the rear wheel 203 r, each approach“0”.

Therefore, the steering angle of the rear wheel 203 r is controlled soas to cause the actual inverted pendulum mass point lateral movementamount and inverted pendulum mass point lateral velocity to converge tothe respective desired values (zero in the present embodiment), whilepreventing the actual steering angle of the rear wheel 203 r fromdiverging from the neutral steering angle (while causing the actualsteering angle to ultimately converge to the neutral steering angle).

Accordingly, the posture of the vehicle body 202 can be stabilizedsmoothly, particularly when the two-wheeled vehicle 201A is stopped ortraveling at a low speed. Further, the two-wheeled vehicle 201A can bestarted smoothly with the vehicle body 202 in a stable posture.

Further, the gains K1 and K2, which are the feedback gains related tothe posture control in the roll direction of the vehicle body 202, arevariably determined, as described above, in accordance with theestimated traveling speed Vox_act, which is an observed value of thecurrent actual traveling speed (transfer velocity in the X-axisdirection) of the two-wheeled vehicle 201A, and the last time's desiredrear-wheel steering angle δr_cmd_p, which is a pseudo estimate of thecurrent actual steering angle of the rear wheel 203 r. Further, thegains K3 and K4, which are the feedback gains related to the control ofthe steering angle of the rear wheel 203 r, are variably determined, asdescribed above, in accordance with the estimated traveling speedVox_act.

Accordingly, when the two-wheeled vehicle 201A is stopped or travelingat a low speed, it is possible to perform the steering of the rear wheel203 r to cause the actual inverted pendulum mass point lateral movementamount of the two-wheeled vehicle 201A to quickly approach the desiredinverted pendulum mass point lateral movement amount Pb_diff_y_cmd.

In the state where the two-wheeled vehicle 201A is traveling at a highspeed, the steering angle of the rear wheel 203 r can readily bemaintained at the neutral steering angle. Further, even if the vehiclebody 202 is leaned, the steering control of the rear wheel 203 r forcausing the actual inverted pendulum mass point lateral movement amountof the two-wheeled vehicle 201A to approach the desired invertedpendulum mass point lateral movement amount Pb_diff_y_cmd is notperformed, or such steering control is restricted. Consequently, a ridercan readily turn the two-wheeled vehicle 201A by banking the vehiclebody 202 by shifting the weight of the rider's body, as with aconventional two-wheeled vehicle.

[Modifications]

Several modifications each related to the aforesaid first or secondembodiment will be described below.

In the first embodiment, the rear wheel 3 r is a non-steering controlwheel. Alternatively, the rear wheel 3 r may be configured to bepassively steered by, for example, the reaction force from the groundsurface 110. In this case, it may be configured such that the estimatedinverted pendulum mass point lateral movement amount Pb_diff_y_act andthe estimated inverted pendulum mass point lateral velocity Vby_act areeach determined to include, not only the component according to thesteering angle δf of the front wheel 3 f, but also the componentaccording to the steering angle δr of the rear wheel 3 r, by theprocessing similar to that in the corresponding one of the estimatedinverted pendulum mass point lateral movement amount calculating section231 and the estimated inverted pendulum mass point lateral velocitycalculating section 232 in the second embodiment.

Further, in each of the aforesaid embodiments, as the motional statequantity of the inverted pendulum mass point 123, which is a constituentelement of the controlled state quantities, the inverted pendulum masspoint lateral movement amount Pb_diff_y and the inverted pendulum masspoint lateral velocity Vby were used. Alternatively, the steeringactuator (front-wheel steering actuator 8 or rear-wheel steeringactuator 208) may be controlled, using only one of the above as thecontrolled state quantity related to the inverted pendulum mass point123, to cause the one state quantity to approach a desired value.

Furthermore, in each of the aforesaid embodiments, as the motional statequantity of the steering angle of the steering control wheel, which isanother constituent element of the controlled state quantities, a valueof the steering angle (δf or δr) and its angular velocity (δf_dot orδr_dot) were used. Alternatively, the steering actuator (front-wheelsteering actuator 8 or rear-wheel steering actuator 208) may becontrolled, using only one of the above as the controlled state quantityrelated to the steering angle of the steering control wheel, to causethe one state quantity to approach a desired value.

The desired value of the motional state quantity of the invertedpendulum mass point 123 (inverted pendulum mass point lateral movementamount Pb_diff_y, inverted pendulum mass point lateral velocity Vby) maybe set to a value other than zero, as long as the value can stabilizethe inverted pendulum mass point 123 and, hence, can stabilize theposture of the vehicle body 2 or 202 (preventing the posture in the rolldirection of the vehicle body 2 or 202 from becoming unstable).

Further, the desired value of the motional state quantity of thesteering angle (steering angle δf or δr, steering angular velocityδf_dot or δr_dot) of the steering control wheel may be set to zero. Itshould be noted that the desired value of the motional state quantity ofthe steering angle of the steering control wheel may be set to a valueother than zero, as long as the value can stabilize the invertedpendulum mass point 123 and, hence, can stabilize the posture of thevehicle body 2 or 202 (preventing the posture in the roll direction ofthe vehicle body 2 or 202 from becoming unstable).

The desired value of the motional state quantity of the invertedpendulum mass point 123 (inverted pendulum mass point lateral movementamount Pb_diff_y, inverted pendulum mass point lateral velocity Vby), orthe desired value of the motional state quantity of the steering angle(steering angle δf or δr, steering angular velocity δf_dot or δr_dot) ofthe steering control wheel, may be set to a value that is determined inaccordance with, for example, the force applied to the steeringhandlebar 7 (or 207) by the rider, or the manipulated variable of thesteering handlebar 7 (or 207).

Further, in each of the aforesaid embodiments, in the processing in theestimated inverted pendulum mass point lateral movement amountcalculating section 31 or 231, the second estimated lateral movementamount component Pb_diff_y_act2 may be calculated as a linear componentwith respect to the steering angle of the front wheel 3 f in the casewhere the magnitude of the actual steering angle of the front wheel 3 fis sufficiently small. Similarly, in the processing in the estimatedinverted pendulum mass point lateral velocity calculating section 32 or232, the second estimated lateral velocity component Vby_act2 may becalculated as a linear component with respect to the steering angle ofthe front wheel 3 f in the case where the magnitude of the actualsteering angle of the front wheel 3 f is sufficiently small.

Further, in the second embodiment, in the processing in the estimatedinverted pendulum mass point lateral movement amount calculating section231, the third estimated lateral movement amount componentPb_diff_y_act3 may be calculated as a linear component with respect tothe steering angle of the rear wheel 203 r in the case where themagnitude of the actual steering angle of the rear wheel 203 r issufficiently small. Similarly, in the processing in the estimatedinverted pendulum mass point lateral velocity calculating section 232,the third estimated lateral velocity component Vby_act3 may becalculated as a linear component with respect to the steering angle ofthe rear wheel 203 r in the case where the magnitude of the actualsteering angle of the rear wheel 203 r is sufficiently small.

In each of the aforesaid embodiments, instead of controlling theinverted pendulum mass point lateral movement amount Pb_diff_y and theinverted pendulum mass point lateral velocity Vby, desired values may beset for the roll angle φb and its angular velocity of the vehicle body 2or 202, and the steering actuator (front-wheel steering actuator 8 orrear-wheel steering actuator 208) may be controlled so as to cause theactual roll angle (detected roll angle φb_act) and its angula velocityof the vehicle body 2 or 202 to approach the desired values, to therebystabilize the posture of the vehicle body 2 or 202.

For example, in the aforesaid expression (55) or (75), instead of thedeviations (Pb_diff_y_cmd−Pb_diff_y_act) and (Vby_cmd−Vby_act), adeviation of the detected roll angle φb_act from the desired value ofthe roll angle of the vehicle body 2 or 202 and a deviation of thedetected value or estimate of the angular velocity (temporal change rateof the detected roll angle φb_act or the like) from the desired value ofthe angular velocity of the roll angle, respectively, may be used todetermine the steering angular acceleration (δf_dot2_cmd or δr_dot2_cmd)as an operational target of the steering actuator (front-wheel steeringactuator 8 or rear-wheel steering actuator 208).

Further, in this case, in determining the desired value of the rollangle φb, the centrifugal force during turning of the two-wheeledvehicle 1A or 201A may be taken into account. That is, the desired valueof the roll angle φb may be determined such that a moment generatedabout the origin of the XYZ coordinate system in the direction about theX axis (roll direction) due to the gravitational force acting on theoverall center of gravity G of the two-wheeled vehicle 1A or 201A and amoment generated about the origin of the XYZ coordinate system in thedirection about the X axis (roll direction) due to the centrifugal forceacting on the overall center of gravity G are balanced (so that the sumof the moments becomes “0”).

In this case, the desired value of the roll angle φb (hereinafter,referred to as “desired roll angle φb_cmd”) can be determined, forexample, in the following manner. Hereinafter, the roll angle φb in thestate where the moments generated about the origin of the XYZ coordinatesystem due to the gravitational force and the centrifugal force actingon the overall center of gravity G are balanced with each other will becalled a “balanced roll angle φb_lean”.

This balanced roll angle φb_lean is obtained approximately by thefollowing expression (81).

φb_lean=−Vox_act*ωz_act/g  (81)

Here, ωz_act represents a turning angular velocity about the verticalaxis (yaw rate) of the vehicle body 2 or 202. For this value, forexample, a detected value of the yaw rate, which is indicated by anoutput from the aforesaid vehicle-body inclination detector 16 or 216including the angular velocity sensor, may be used.

Alternatively, it may be obtained from, for example, an actual value ofthe aforesaid front-wheel effective steering angle δ′f (estimatedfront-wheel effective steering angle δ′f_act), an actual value of therear-wheel effective steering angle δ′r (estimated rear-wheel effectivesteering angle δ′r_act), and an actual value of the traveling speed Vox(estimated traveling speed Vox_act) of the two-wheeled vehicle 1A or201A, by the following expression (82).

ωz_act=Vox_act*((Lr/L)*tan(δ′f_act)−(Lf/L)*tan(δ′r_act))  (82)

In the case where the rear wheel 3 r is a non-steering control wheel, asin the aforesaid first embodiment, the computation of the expression(82) can be performed by setting: δ′r_act=0.

The balanced roll angle φb_lean calculated in the above-described mannermay be determined as a desired value of the desired roll angle φb_cmd.Alternatively, a value obtained by multiplying φb_lean by a positiveconstant of 1 or less may be determined as the desired roll angleφb_cmd.

The desired roll angle φb_cmd may be “0” when the two-wheeled vehicle 1Aor 201A is stopped before it starts moving, or when the traveling speedVox of the vehicle is sufficiently low.

Further, the desired value of the angular velocity of the roll angle φbmay be set to zero. It should be noted that the desired value of theangular velocity of the roll angle φb may be set to a value other thanzero, as long as the value can stabilize the posture of the vehicle body2 or 202 (preventing the posture in the roll direction of the vehiclebody 2 or 202 from becoming unstable).

For example, the desired value of the angular velocity of the roll angleφb may be determined in accordance with the force applied to thesteering handlebar 7 (or 207) by the rider or the manipulated variableof the steering handlebar 7 (or 207).

In each of the aforesaid embodiments, in the processing in the posturecontrol arithmetic section 37 or 237, the desired front-wheel steeringangular acceleration δf_dot2_cmd or desired rear-wheel steering angularacceleration δr_dot2_cmd was determined as an operational target of thesteering actuator (front-wheel steering actuator 8 or rear-wheelsteering actuator 208).

In the processing in the posture control arithmetic section 37 in thefirst embodiment, however, a desired value of the torque about thesteering axis Csf of the steering control wheel (front wheel 3 f) may bedetermined in place of, or in addition to, the desired front-wheelsteering angular acceleration δf_dot2_cmd. Then, in the aforesaidfront-wheel steering actuator control section 41, the driving force(torque) of the front-wheel steering actuator 8 may be controlled tocause the actual torque about the steering axis Csf to match the desiredvalue.

Similarly, in the processing in the posture control arithmetic section237 in the second embodiment, a desired value of the torque about thesteering axis Csr of the steering control wheel (rear wheel 203 r) maybe determined in place of, or in addition to, the desired rear-wheelsteering angular acceleration δr_dot2_cmd. Then, in the aforesaidrear-wheel steering actuator control section 241, the driving force(torque) of the rear-wheel steering actuator 208 may be controlled tocause the actual torque about the steering axis Csr to match the desiredvalue.

Further, in the first embodiment, the arrangement of the steering axisCsf of the front wheel 3 f was set such that the height a of theaforesaid intersection point Ef takes a negative value (such that theintersection point Ef is below the ground surface 110). Alternatively,the arrangement of the steering axis Csf of the front wheel 3 f may beset such that, in the state where the intersection point Ef is above theground surface 110, a<a_sum or a≦a_s holds for a_sum defined by theaforesaid expression (28) or for a_s defined by the aforesaid expression(40).

Similarly, in the second embodiment, the arrangement of the steeringaxis Csr of the rear wheel 203 r may be set such that, in the statewhere the intersection point Er′ is above the ground surface 110, forthe height a′ of the intersection point Er′, a′<a_sum′ or a′≦a_s′ holdsfor a_sum′ defined by the aforesaid expression (28)′ or for a_s′ definedby the aforesaid expression (40)′.

Supplementally, the total mass m, the overall inertia I, and the heighth of the overall center of gravity G of the two-wheeled vehicle 1A or201A will vary to some extent when there is an object mounted on thetwo-wheeled vehicle 1A or 201A.

In this case, in the two-wheeled vehicle 1A of the first embodiment, aminimum value for a_sum defined by the aforesaid expression (28) or aminimum value for a_s defined by the aforesaid expression (40) may beobtained in advance within the range of variation estimated for each ofm, I, and h.

Then, the arrangement position of the steering axis Csf of the frontwheel 3 f may be set such that the height a of the intersection point Efbecomes smaller than the minimum value of a_sum or not greater than theminimum value of a_s.

Similarly, in the two-wheeled vehicle 201A of the second embodiment, aminimum value for a_sum′ defined by the aforesaid expression (28)′ or aminimum value for a_s′ defined by the aforesaid expression (40)′ may beobtained in advance within the range of variation estimated for each ofm, I, and h.

Then, the arrangement position of the steering axis Csr of the rearwheel 203 r may be set such that the height a′ of the intersection pointEr′ becomes smaller than the minimum value of a_sum′ or not greater thanthe minimum value of a_s′.

It should be noted that the minimum value of a_sum or a_s in thetwo-wheeled vehicle 1A, or the minimum value of a_sum′ or a_s′ in thetwo-wheeled vehicle 201A, may be obtained under the condition that noperson or article has been mounted on the two-wheeled vehicle 1A or201A.

Further, in each of the aforesaid embodiments, the description was madeby giving, as an example, the case where the mass and the inertia momentwere set only for the vehicle body 2 or 202. The mass or the inertiamoment, however, may also be set for the steering control wheel, asexplained previously with reference to FIGS. 13 and 14. In such a caseas well, the equivalent transformation explained above may be performedto attain a system made up of the inverted pendulum mass point (masspoint A) and the ground surface mass point (mass point B), so that theposture of the vehicle body 2 or 202 can be controlled as in each of theaforesaid embodiments.

Further, similarly to a case where a variable related to the position ofa mass point may be converted to a variable related to the angle of theline segment connecting the mass point and the origin, any one of thevariables and constants used in the embodiments may be replaced withanother variable or constant that has a one-to-one relationshiptherewith. Any variables or constants for which such replacement ispossible can be regarded as equivalent to each other.

Furthermore, for any of the techniques, means, and algorithms shown inthe embodiments, one that has been equivalently transformed to producethe same result can be regarded as the same.

What is claimed is:
 1. A mobile vehicle having a vehicle body and afront wheel and a rear wheel arranged spaced apart from each other in alongitudinal direction of the vehicle body, one of the front wheel andthe rear wheel being a steering control wheel which can be steered abouta steering axis tilted backward, the mobile vehicle comprising: asteering actuator which generates a steering force for steering thesteering control wheel; and a control device which controls the steeringactuator so as to stabilize a posture of the vehicle body in accordancewith at least an observed value of an inclination angle in a rolldirection of the vehicle body, wherein in a case where a state in whichthe front wheel and the rear wheel of the mobile vehicle are bothstationary in an upright posture in contact with a ground surface andaxle centerlines of the front wheel and the rear wheel extend inparallel with each other in a direction orthogonal to the longitudinaldirection of the vehicle body is defined as a basic posture state, theheight a, from the ground surface, of a point of intersection of thesteering axis of the steering control wheel and a virtual straight lineconnecting a ground contact point of the steering control wheel and thecenter of axle of the steering control wheel in the basic posture stateis set to satisfy the following first condition: First Condition: in asystem made up of a mass point A, which moves in a horizontal directionabove the ground surface, with which the mobile vehicle comes intocontact, in accordance with the inclination angle in the roll directionof the vehicle body and the steering angle of the steering controlwheel, and a mass point B, which moves horizontally on the groundsurface, with which the mobile vehicle comes into contact, in accordancewith the steering angle of the steering control wheel, independently ofthe inclination angle in the roll direction of the vehicle body, thesystem having a mass of the mass point A, a mass of the mass point B, aheight of the mass point A from the ground surface, a relationship amongan inclination angle in the roll direction of the vehicle body, asteering angle of the steering control wheel, and a displacement of themass point A, and a relationship between a steering angle of thesteering control wheel and a displacement of the mass point B which areset to have dynamic characteristics equivalent to those of dynamics ofthe mobile vehicle in the case where the steering control wheel of themobile vehicle being stationary on a prescribed origin in the basicposture state is steered by a steering angle δ, the system being alsoconfigured such that the mass point A accelerates or decelerates inresponse to a first gravitational moment, generated about the origin dueto a gravitational force acting on the mass point A, a secondgravitational moment, generated about the origin due to a gravitationalforce acting on the mass point B, and a road surface reaction forcemoment, acting about the origin due to a road surface reaction force inthe vertical direction which acts on the center of contact pressure ofthe front wheel and the rear wheel of the mobile vehicle as a whole, inthe case where a steering angle of the steering control wheel at thetime when the steering control wheel is steered to cause a front end ofthe steering control wheel to turn left as the mobile vehicle in thebasic posture state is seen from above is defined as a positive steeringangle and in the case where a moment that causes the vehicle body tolean to the right is defined as a positive moment, the following holds:Mp/δ>−M2/δ where M2 denotes the second gravitational moment generated bymovement of the mass point B at the time when the steering control wheelof the mobile vehicle being stationary on the origin in the basicposture state is steered instantaneously by the steering angle δ, and Mpdenotes the road surface reaction force moment generated about theorigin by movement of the center of contact pressure at the time whenthe steering control wheel of the mobile vehicle being stationary on theorigin in the basis posture state is steered instantaneously by thesteering angle δ.
 2. The mobile vehicle according to claim 1, wherein,to satisfy the first condition, the height a is set to be smaller than afirst prescribed value a_sum determined by the following expression (A):a_sum=((h+(I/m)/h)/(Rg+(I/m)/h))×Rs  (A) where polarity of a: a>0 in thecase where the point of intersection is above the ground surface, a<0 inthe case where the point of intersection is below the ground surface; I:inertia moment of the mobile vehicle; m: mass of the mobile vehicle; h:height of the center of gravity of the mobile vehicle from the groundsurface in the basic posture state of the mobile vehicle;Rg≡(Lr/(Lf+Lr))×Rf+(Lf/(Lf+Lr))×Rr; Lf: longitudinal distance betweenthe center of gravity of the mobile vehicle and the center of axle ofthe front wheel in the basic posture state of the mobile vehicle; Lr:longitudinal distance between the center of gravity of the mobilevehicle and the center of axle of the rear wheel in the basic posturestate of the mobile vehicle; Rf: radius of curvature of a transversecross-sectional shape of the front wheel at a ground contact point ofthe front wheel in the basic posture state of the mobile vehicle; Rr:radius of curvature of a transverse cross-sectional shape of the rearwheel at a ground contact point of the rear wheel in the basic posturestate of the mobile vehicle; and Rs: one of the radii of curvature Rfand Rr that corresponds to the steering control wheel.
 3. The mobilevehicle according to claim 1, wherein the height a is set to furthersatisfy the following second condition: Second Condition:Msum/δ>−M2/δ where Msum denotes a sum moment of the second gravitationalmoment M2 and the road surface reaction force moment Mp.
 4. The mobilevehicle according to claim 3, wherein, to satisfy the first conditionand the second condition, the height a is set to be not greater than asecond prescribed value a_s determined by the following expression (B):a _(—) s=((h+(I/m)/h)/(Rg+2×(I/m)/h))×Rs  (B) where polarity of a: a>0in the case where the point of intersection is above the ground surface,a<0 in the case where the point of intersection is below the groundsurface; I: inertia moment of the mobile vehicle; m: mass of the mobilevehicle; h: height of the center of gravity of the mobile vehicle fromthe ground surface in the basic posture state of the mobile vehicle;Rg≡(Lr/(Lf+Lr))×Rf+(Lf/(Lf+Lr))×Rr; Lf: longitudinal distance betweenthe center of gravity of the mobile vehicle and the center of axle ofthe front wheel in the basic posture state of the mobile vehicle; Lr:longitudinal distance between the center of gravity of the mobilevehicle and the center of axle of the rear wheel in the basic posturestate of the mobile vehicle; Rf: radius of curvature of a transversecross-sectional shape of the front wheel at a ground contact point ofthe front wheel in the basic posture state of the mobile vehicle; Rr:radius of curvature of a transverse cross-sectional shape of the rearwheel at a ground contact point of the rear wheel in the basic posturestate of the mobile vehicle; and Rs: one of the radii of curvature Rfand Rr that corresponds to the steering control wheel.
 5. A mobilevehicle having a vehicle body and a front wheel and a rear wheelarranged spaced apart from each other in a longitudinal direction of thevehicle body, one of the front wheel and the rear wheel being a steeringcontrol wheel which can be steered about a steering axis tiltedbackward, the mobile vehicle comprising: a steering actuator whichgenerates a driving force for steering the steering control wheel; and acontrol device which controls the steering actuator so as to stabilize aposture of the vehicle body in accordance with at least an observedvalue of an inclination angle in a roll direction of the vehicle body,wherein in the case where a state in which the front wheel and the rearwheel of the mobile vehicle are both stationary in an upright posture incontact with a ground surface and axle centerlines of the front wheeland the rear wheel extend in parallel with each other in a directionorthogonal to the longitudinal direction of the vehicle body is definedas a basic posture state and in the case where a radius of curvature ofa transverse cross-sectional shape of the steering control wheel at aground contact point of the steering control wheel in the basic posturestate of the mobile vehicle is denoted as Rs, the height a, from theground surface, of a point of intersection of the steering axis of thesteering control wheel and a virtual straight line connecting the groundcontact point of the steering control wheel and the center of axle ofthe steering control wheel in the basic posture state is set to be nothigher than the radius of curvature Rs.
 6. The mobile vehicle accordingto claim 5, wherein the height a is set to a level below the groundsurface.